24=10x^2+27x

Solution for 24=10x^2+27x equation:

24=10x^2+27x

We move all terms to the left:

24-(10x^2+27x)=0

We get rid of parentheses

-10x^2-27x+24=0

a = -10; b = -27; c = +24;
Δ = b2-4ac
Δ = -272-4·(-10)·24
Δ = 1689
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{-(-27)-\sqrt{1689}}{2*-10}=\frac{27-\sqrt{1689}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{1689}}{2*-10}=\frac{27+\sqrt{1689}}{-20}
$