18x^2-9=-21x

Solution for 18x^2-9=-21x equation:

18x^2-9=-21x

We move all terms to the left:

18x^2-9-(-21x)=0

We get rid of parentheses

18x^2+21x-9=0

a = 18; b = 21; c = -9;
Δ = b2-4ac
Δ = 212-4·18·(-9)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-33}{2*18}=\frac{-54}{36}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+33}{2*18}=\frac{12}{36}
=1/3
$