9x+30+x^2+2x+20=5x^2+30

Solution for 9x+30+x^2+2x+20=5x^2+30 equation:

9x+30+x^2+2x+20=5x^2+30

We move all terms to the left:

9x+30+x^2+2x+20-(5x^2+30)=0

We add all the numbers together, and all the variables

x^2+11x-(5x^2+30)+50=0

We get rid of parentheses

x^2-5x^2+11x-30+50=0

We add all the numbers together, and all the variables

-4x^2+11x+20=0

a = -4; b = 11; c = +20;
Δ = b2-4ac
Δ = 112-4·(-4)·20
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-21}{2*-4}=\frac{-32}{-8}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+21}{2*-4}=\frac{10}{-8}
=-1+1/4
$