6^2+x^2=7.5^2

Solution for 6^2+x^2=7.5^2 equation:

6^2+x^2=7.5^2

We move all terms to the left:

6^2+x^2-(7.5^2)=0

We add all the numbers together, and all the variables

x^2-20.25=0

a = 1; b = 0; c = -20.25;
Δ = b2-4ac
Δ = 02-4·1·(-20.25)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-9}{2*1}=\frac{-9}{2}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+9}{2*1}=\frac{9}{2}
=4+1/2
$