3a^2=18a-7

Solution for 3a^2=18a-7 equation:

3a^2=18a-7

We move all terms to the left:

3a^2-(18a-7)=0

We get rid of parentheses

3a^2-18a+7=0

a = 3; b = -18; c = +7;
Δ = b2-4ac
Δ = -182-4·3·7
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{15}}{2*3}=\frac{18-4\sqrt{15}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{15}}{2*3}=\frac{18+4\sqrt{15}}{6}
$