5a^2-18=-6a

Solution for 5a^2-18=-6a equation:

5a^2-18=-6a

We move all terms to the left:

5a^2-18-(-6a)=0

We get rid of parentheses

5a^2+6a-18=0

a = 5; b = 6; c = -18;
Δ = b2-4ac
Δ = 62-4·5·(-18)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{11}}{2*5}=\frac{-6-6\sqrt{11}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{11}}{2*5}=\frac{-6+6\sqrt{11}}{10}
$