(2x-5)(2x+5)-2x*x=75

Solution for (2x-5)(2x+5)-2x*x=75 equation:

(2x-5)(2x+5)-2x*x=75

We move all terms to the left:

(2x-5)(2x+5)-2x*x-(75)=0

We use the square of the difference formula

4x^2-2x*x-25-75=0

Wy multiply elements

4x^2-2x^2-25-75=0

We add all the numbers together, and all the variables

2x^2-100=0

a = 2; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·2·(-100)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*2}=\frac{0-20\sqrt{2}}{4}
=-\frac{20\sqrt{2}}{4}
=-5\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*2}=\frac{0+20\sqrt{2}}{4}
=\frac{20\sqrt{2}}{4}
=5\sqrt{2}
$