-5x^2=23x+24

Solution for -5x^2=23x+24 equation:

-5x^2=23x+24

We move all terms to the left:

-5x^2-(23x+24)=0

We get rid of parentheses

-5x^2-23x-24=0

a = -5; b = -23; c = -24;
Δ = b2-4ac
Δ = -232-4·(-5)·(-24)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-7}{2*-5}=\frac{16}{-10}
=-1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+7}{2*-5}=\frac{30}{-10}
=-3
$