30x+18=-5x^2

Solution for 30x+18=-5x^2 equation:

30x+18=-5x^2

We move all terms to the left:

30x+18-(-5x^2)=0

We get rid of parentheses

5x^2+30x+18=0

a = 5; b = 30; c = +18;
Δ = b2-4ac
Δ = 302-4·5·18
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{15}}{2*5}=\frac{-30-6\sqrt{15}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{15}}{2*5}=\frac{-30+6\sqrt{15}}{10}
$