Solve for: x-5(x-1)=x * (2x-3)

Expression: $x-5\left( x-1 \right)=x \times \left( 2x-3 \right)$

Distribute $-5$ through the parentheses

$x-5x+5=x \times \left( 2x-3 \right)$

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

$\begin{align*}&\begin{array} { l }x_1=\frac{ -1-\sqrt{ 41 } }{ 4 },& x_2=\frac{ -1+\sqrt{ 41 } }{ 4 }\end{array} \\&\begin{array} { l }x_1\approx-1.85078,& x_2\approx1.35078\end{array}\end{align*}$