24x^2+52x+24=90

Solution for 24x^2+52x+24=90 equation:

24x^2+52x+24=90

We move all terms to the left:

24x^2+52x+24-(90)=0

We add all the numbers together, and all the variables

24x^2+52x-66=0

a = 24; b = 52; c = -66;
Δ = b2-4ac
Δ = 522-4·24·(-66)
Δ = 9040
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:

$\sqrt{\Delta}=\sqrt{9040}=\sqrt{16*565}=\sqrt{16}*\sqrt{565}=4\sqrt{565}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{565}}{2*24}=\frac{-52-4\sqrt{565}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{565}}{2*24}=\frac{-52+4\sqrt{565}}{48}
$