18x2-57x=-30

Solution for 18x2-57x=-30 equation:

18x^2-57x=-30

We move all terms to the left:

18x^2-57x-(-30)=0

We add all the numbers together, and all the variables

18x^2-57x+30=0

a = 18; b = -57; c = +30;
Δ = b2-4ac
Δ = -572-4·18·30
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{-(-57)-33}{2*18}=\frac{24}{36}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+33}{2*18}=\frac{90}{36}
=2+1/2
$