57=24x^2+25x

Solution for 57=24x^2+25x equation:

57=24x^2+25x

We move all terms to the left:

57-(24x^2+25x)=0

We get rid of parentheses

-24x^2-25x+57=0

a = -24; b = -25; c = +57;
Δ = b2-4ac
Δ = -252-4·(-24)·57
Δ = 6097
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-\sqrt{6097}}{2*-24}=\frac{25-\sqrt{6097}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{6097}}{2*-24}=\frac{25+\sqrt{6097}}{-48}
$