x^2+6x+9+4x^2-24x+36=30

Solution for x^2+6x+9+4x^2-24x+36=30 equation:

x^2+6x+9+4x^2-24x+36=30

We move all terms to the left:

x^2+6x+9+4x^2-24x+36-(30)=0

We add all the numbers together, and all the variables

5x^2-18x+15=0

a = 5; b = -18; c = +15;
Δ = b2-4ac
Δ = -182-4·5·15
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{6}}{2*5}=\frac{18-2\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{6}}{2*5}=\frac{18+2\sqrt{6}}{10}
$