$$21x-84+21x=10x\left(x-4\right)$$
Combine $21x$ and $21x$ to get $42x$.$$42x-84=10x\left(x-4\right)$$
Use the distributive property to multiply $10x$ by $x-4$.$$42x-84=10x^{2}-40x$$
Subtract $10x^{2}$ from both sides.$$42x-84-10x^{2}=-40x$$
Add $40x$ to both sides.$$42x-84-10x^{2}+40x=0$$
Combine $42x$ and $40x$ to get $82x$.$$82x-84-10x^{2}=0$$
All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. The quadratic formula gives two solutions, one when $±$ is addition and one when it is subtraction.$$-10x^{2}+82x-84=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $-10$ for $a$, $82$ for $b$, and $-84$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.$$x=\frac{-82±\sqrt{82^{2}-4\left(-10\right)\left(-84\right)}}{2\left(-10\right)}$$
Square $82$.$$x=\frac{-82±\sqrt{6724-4\left(-10\right)\left(-84\right)}}{2\left(-10\right)}$$
Multiply $-4$ times $-10$.$$x=\frac{-82±\sqrt{6724+40\left(-84\right)}}{2\left(-10\right)}$$
Multiply $40$ times $-84$.$$x=\frac{-82±\sqrt{6724-3360}}{2\left(-10\right)}$$
Add $6724$ to $-3360$.$$x=\frac{-82±\sqrt{3364}}{2\left(-10\right)}$$
Take the square root of $3364$.$$x=\frac{-82±58}{2\left(-10\right)}$$
Multiply $2$ times $-10$.$$x=\frac{-82±58}{-20}$$
Now solve the equation $x=\frac{-82±58}{-20}$ when $±$ is plus. Add $-82$ to $58$.$$x=\frac{-24}{-20}$$
Reduce the fraction $\frac{-24}{-20}$ to lowest terms by extracting and canceling out $4$.$$x=\frac{6}{5}$$
Now solve the equation $x=\frac{-82±58}{-20}$ when $±$ is minus. Subtract $58$ from $-82$.$$x=\frac{-140}{-20}$$
Divide $-140$ by $-20$.$$x=7$$
The equation is now solved.$$x=\frac{6}{5}$$ $$x=7$$