x(x-5)-62=-5x+82

Solution for x(x-5)-62=-5x+82 equation:

x(x-5)-62=-5x+82

We move all terms to the left:

x(x-5)-62-(-5x+82)=0

We multiply parentheses

x^2-5x-(-5x+82)-62=0

We get rid of parentheses

x^2-5x+5x-82-62=0

We add all the numbers together, and all the variables

x^2-144=0

a = 1; b = 0; c = -144;
Δ = b2-4ac
Δ = 02-4·1·(-144)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*1}=\frac{-24}{2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*1}=\frac{24}{2}
=12
$