18=-6x^2+24x

Solution for 18=-6x^2+24x equation:

18=-6x^2+24x

We move all terms to the left:

18-(-6x^2+24x)=0

We get rid of parentheses

6x^2-24x+18=0

a = 6; b = -24; c = +18;
Δ = b2-4ac
Δ = -242-4·6·18
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12}{2*6}=\frac{12}{12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12}{2*6}=\frac{36}{12}
=3
$