$x-5x+5=x \times \left( 2x-3 \right)$
Distribute $x$ through the parentheses$x-5x+5=2{x}^{2}-3x$
Collect like terms$-4x+5=2{x}^{2}-3x$
Move the variables to the left-hand side and change their signs$-4x+5-2{x}^{2}+3x=0$
Collect like terms$-x+5-2{x}^{2}=0$
Use the commutative property to reorder the terms$-2{x}^{2}-x+5=0$
Change the signs on both sides of the equation$2{x}^{2}+x-5=0$
Identify the coefficients $a$, $b$ and $c$ of the quadratic equation$\begin{array} { l }a=2,& b=1,& c=-5\end{array}$
Substitute $a=2$, $b=1$ and $c=-5$ into the quadratic formula $x=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$$x=\frac{ -1\pm\sqrt{ {1}^{2}-4 \times 2 \times \left( -5 \right) } }{ 2 \times 2 }$
$1$ raised to any power equals $1$$x=\frac{ -1\pm\sqrt{ 1-4 \times 2 \times \left( -5 \right) } }{ 2 \times 2 }$
Calculate the product$x=\frac{ -1\pm\sqrt{ 1+40 } }{ 2 \times 2 }$
Multiply the numbers$x=\frac{ -1\pm\sqrt{ 1+40 } }{ 4 }$
Add the numbers$x=\frac{ -1\pm\sqrt{ 41 } }{ 4 }$
Write the solutions, one with a $+$ sign and one with a $-$ sign$\begin{array} { l }x=\frac{ -1+\sqrt{ 41 } }{ 4 },\\x=\frac{ -1-\sqrt{ 41 } }{ 4 }\end{array}$
The equation has $2$ solutions$\begin{align*}&\begin{array} { l }x_1=\frac{ -1-\sqrt{ 41 } }{ 4 },& x_2=\frac{ -1+\sqrt{ 41 } }{ 4 }\end{array} \\&\begin{array} { l }x_1\approx-1.85078,& x_2\approx1.35078\end{array}\end{align*}$