(x+5)(x-5)=4x-10

Solution for (x+5)(x-5)=4x-10 equation:

(x+5)(x-5)=4x-10

We move all terms to the left:

(x+5)(x-5)-(4x-10)=0

We use the square of the difference formula

x^2-(4x-10)-25=0

We get rid of parentheses

x^2-4x+10-25=0

We add all the numbers together, and all the variables

x^2-4x-15=0

a = 1; b = -4; c = -15;
Δ = b2-4ac
Δ = -42-4·1·(-15)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{19}}{2*1}=\frac{4-2\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{19}}{2*1}=\frac{4+2\sqrt{19}}{2}
$