3x2+21=18x

Solution for 3x2+21=18x equation:

3x^2+21=18x

We move all terms to the left:

3x^2+21-(18x)=0

a = 3; b = -18; c = +21;
Δ = b2-4ac
Δ = -182-4·3·21
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{2}}{2*3}=\frac{18-6\sqrt{2}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{2}}{2*3}=\frac{18+6\sqrt{2}}{6}
$