30x=-9x^2+6

Solution for 30x=-9x^2+6 equation:

30x=-9x^2+6

We move all terms to the left:

30x-(-9x^2+6)=0

We get rid of parentheses

9x^2+30x-6=0

a = 9; b = 30; c = -6;
Δ = b2-4ac
Δ = 302-4·9·(-6)
Δ = 1116
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:

$\sqrt{\Delta}=\sqrt{1116}=\sqrt{36*31}=\sqrt{36}*\sqrt{31}=6\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{31}}{2*9}=\frac{-30-6\sqrt{31}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{31}}{2*9}=\frac{-30+6\sqrt{31}}{18}
$