24^2+x^2=74^2

Solution for 24^2+x^2=74^2 equation:

24^2+x^2=74^2

We move all terms to the left:

24^2+x^2-(74^2)=0

We add all the numbers together, and all the variables

x^2-4900=0

a = 1; b = 0; c = -4900;
Δ = b2-4ac
Δ = 02-4·1·(-4900)
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-140}{2*1}=\frac{-140}{2}
=-70
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+140}{2*1}=\frac{140}{2}
=70
$