24^2+10x^2=74^2

Solution for 24^2+10x^2=74^2 equation:

24^2+10x^2=74^2

We move all terms to the left:

24^2+10x^2-(74^2)=0

We add all the numbers together, and all the variables

10x^2-4900=0

a = 10; b = 0; c = -4900;
Δ = b2-4ac
Δ = 02-4·10·(-4900)
Δ = 196000
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:

$\sqrt{\Delta}=\sqrt{196000}=\sqrt{19600*10}=\sqrt{19600}*\sqrt{10}=140\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-140\sqrt{10}}{2*10}=\frac{0-140\sqrt{10}}{20}
=-\frac{140\sqrt{10}}{20}
=-7\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+140\sqrt{10}}{2*10}=\frac{0+140\sqrt{10}}{20}
=\frac{140\sqrt{10}}{20}
=7\sqrt{10}
$