5(x+10)(x-10)=75x

Solution for 5(x+10)(x-10)=75x equation:

5(x+10)(x-10)=75x

We move all terms to the left:

5(x+10)(x-10)-(75x)=0

We add all the numbers together, and all the variables

-75x+5(x+10)(x-10)=0

We use the square of the difference formula

x^2-75x-100=0

a = 1; b = -75; c = -100;
Δ = b2-4ac
Δ = -752-4·1·(-100)
Δ = 6025
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:

$\sqrt{\Delta}=\sqrt{6025}=\sqrt{25*241}=\sqrt{25}*\sqrt{241}=5\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{241}}{2*1}=\frac{75-5\sqrt{241}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{241}}{2*1}=\frac{75+5\sqrt{241}}{2}
$