18x^2-7=4

Solution for 18x^2-7=4 equation:

18x^2-7=4

We move all terms to the left:

18x^2-7-(4)=0

We add all the numbers together, and all the variables

18x^2-11=0

a = 18; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·18·(-11)
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{22}}{2*18}=\frac{0-6\sqrt{22}}{36}
=-\frac{6\sqrt{22}}{36}
=-\frac{\sqrt{22}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{22}}{2*18}=\frac{0+6\sqrt{22}}{36}
=\frac{6\sqrt{22}}{36}
=\frac{\sqrt{22}}{6}
$