24a^2+120=164a

Solution for 24a^2+120=164a equation:

24a^2+120=164a

We move all terms to the left:

24a^2+120-(164a)=0

a = 24; b = -164; c = +120;
Δ = b2-4ac
Δ = -1642-4·24·120
Δ = 15376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15376}=124$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-164)-124}{2*24}=\frac{40}{48}
=5/6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-164)+124}{2*24}=\frac{288}{48}
=6
$