x(2x-3)-(5-x)=83

Solution for x(2x-3)-(5-x)=83 equation:

x(2x-3)-(5-x)=83

We move all terms to the left:

x(2x-3)-(5-x)-(83)=0

We add all the numbers together, and all the variables

x(2x-3)-(-1x+5)-83=0

We multiply parentheses

2x^2-3x-(-1x+5)-83=0

We get rid of parentheses

2x^2-3x+1x-5-83=0

We add all the numbers together, and all the variables

2x^2-2x-88=0

a = 2; b = -2; c = -88;
Δ = b2-4ac
Δ = -22-4·2·(-88)
Δ = 708
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{708}=\sqrt{4*177}=\sqrt{4}*\sqrt{177}=2\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{177}}{2*2}=\frac{2-2\sqrt{177}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{177}}{2*2}=\frac{2+2\sqrt{177}}{4}
$