(x+5)(x-5)=37.5

Solution for (x+5)(x-5)=37.5 equation:

(x+5)(x-5)=37.5

We move all terms to the left:

(x+5)(x-5)-(37.5)=0

We add all the numbers together, and all the variables

(x+5)(x-5)-37.5=0

We use the square of the difference formula

x^2-25-37.5=0

We add all the numbers together, and all the variables

x^2-62.5=0

a = 1; b = 0; c = -62.5;
Δ = b2-4ac
Δ = 02-4·1·(-62.5)
Δ = 250
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:

$\sqrt{\Delta}=\sqrt{250}=\sqrt{25*10}=\sqrt{25}*\sqrt{10}=5\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-5\sqrt{10}}{2*1}=\frac{0-5\sqrt{10}}{2}
=-\frac{5\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+5\sqrt{10}}{2*1}=\frac{0+5\sqrt{10}}{2}
=\frac{5\sqrt{10}}{2}
$