66x=24-18x2

Solution for 66x=24-18x2 equation:

66x=24-18x^2

We move all terms to the left:

66x-(24-18x^2)=0

We get rid of parentheses

18x^2+66x-24=0

a = 18; b = 66; c = -24;
Δ = b2-4ac
Δ = 662-4·18·(-24)
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-78}{2*18}=\frac{-144}{36}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+78}{2*18}=\frac{12}{36}
=1/3
$