(x-5)(x+5)=7x+5

Solution for (x-5)(x+5)=7x+5 equation:

(x-5)(x+5)=7x+5

We move all terms to the left:

(x-5)(x+5)-(7x+5)=0

We use the square of the difference formula

x^2-(7x+5)-25=0

We get rid of parentheses

x^2-7x-5-25=0

We add all the numbers together, and all the variables

x^2-7x-30=0

a = 1; b = -7; c = -30;
Δ = b2-4ac
Δ = -72-4·1·(-30)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*1}=\frac{20}{2}
=10
$