Calculate: k=2
k = 12/5 = 2 2/5 = 2.4

Solve for k: $k=2$
$k = \frac{12}{5} = 2\frac{2}{5} = 2.4$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(5k-7\right)^{2}$.

$$25k^{2}-70k+49-8\left(5k-7\right)+15=0$$

Use the distributive property to multiply $-8$ by $5k-7$.

$$25k^{2}-70k+49-40k+56+15=0$$

Combine $-70k$ and $-40k$ to get $-110k$.

$$25k^{2}-110k+49+56+15=0$$

Add $49$ and $56$ to get $105$.

$$25k^{2}-110k+105+15=0$$

Add $105$ and $15$ to get $120$.

$$25k^{2}-110k+120=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $25$ for $a$, $-110$ for $b$, and $120$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$k=\frac{-\left(-110\right)±\sqrt{\left(-110\right)^{2}-4\times 25\times 120}}{2\times 25}$$

Square $-110$.

$$k=\frac{-\left(-110\right)±\sqrt{12100-4\times 25\times 120}}{2\times 25}$$

Multiply $-4$ times $25$.

$$k=\frac{-\left(-110\right)±\sqrt{12100-100\times 120}}{2\times 25}$$

Multiply $-100$ times $120$.

$$k=\frac{-\left(-110\right)±\sqrt{12100-12000}}{2\times 25}$$

Add $12100$ to $-12000$.

$$k=\frac{-\left(-110\right)±\sqrt{100}}{2\times 25}$$

Take the square root of $100$.

$$k=\frac{-\left(-110\right)±10}{2\times 25}$$

The opposite of $-110$ is $110$.

$$k=\frac{110±10}{2\times 25}$$

Multiply $2$ times $25$.

$$k=\frac{110±10}{50}$$

Now solve the equation $k=\frac{110±10}{50}$ when $±$ is plus. Add $110$ to $10$.

$$k=\frac{120}{50}$$

Reduce the fraction $\frac{120}{50}$ to lowest terms by extracting and canceling out $10$.

$$k=\frac{12}{5}$$

Now solve the equation $k=\frac{110±10}{50}$ when $±$ is minus. Subtract $10$ from $110$.

$$k=\frac{100}{50}$$

Divide $100$ by $50$.

$$k=2$$

The equation is now solved.

$$k=\frac{12}{5}$$ $$k=2$$