18x^2-3=5x

Solution for 18x^2-3=5x equation:

18x^2-3=5x

We move all terms to the left:

18x^2-3-(5x)=0

a = 18; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·18·(-3)
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{241}}{2*18}=\frac{5-\sqrt{241}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{241}}{2*18}=\frac{5+\sqrt{241}}{36}
$