a^2=7.5^2-5^2

Solution for a^2=7.5^2-5^2 equation:

a^2=7.5^2-5^2

We move all terms to the left:

a^2-(7.5^2-5^2)=0

We add all the numbers together, and all the variables

a^2-31.25=0

a = 1; b = 0; c = -31.25;
Δ = b2-4ac
Δ = 02-4·1·(-31.25)
Δ = 125
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-5\sqrt{5}}{2*1}=\frac{0-5\sqrt{5}}{2}
=-\frac{5\sqrt{5}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+5\sqrt{5}}{2*1}=\frac{0+5\sqrt{5}}{2}
=\frac{5\sqrt{5}}{2}
$