18x^2-27=-45x

Solution for 18x^2-27=-45x equation:

18x^2-27=-45x

We move all terms to the left:

18x^2-27-(-45x)=0

We get rid of parentheses

18x^2+45x-27=0

a = 18; b = 45; c = -27;
Δ = b2-4ac
Δ = 452-4·18·(-27)
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-63}{2*18}=\frac{-108}{36}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+63}{2*18}=\frac{18}{36}
=1/2
$