30x^2-33-18=0

Solution for 30x^2-33-18=0 equation:

30x^2-33-18=0

We add all the numbers together, and all the variables

30x^2-51=0

a = 30; b = 0; c = -51;
Δ = b2-4ac
Δ = 02-4·30·(-51)
Δ = 6120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6120}=\sqrt{36*170}=\sqrt{36}*\sqrt{170}=6\sqrt{170}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{170}}{2*30}=\frac{0-6\sqrt{170}}{60}
=-\frac{6\sqrt{170}}{60}
=-\frac{\sqrt{170}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{170}}{2*30}=\frac{0+6\sqrt{170}}{60}
=\frac{6\sqrt{170}}{60}
=\frac{\sqrt{170}}{10}
$