6x+30-3x^2-12x+15=5x^2+30x+25

Solution for 6x+30-3x^2-12x+15=5x^2+30x+25 equation:

6x+30-3x^2-12x+15=5x^2+30x+25

We move all terms to the left:

6x+30-3x^2-12x+15-(5x^2+30x+25)=0

We add all the numbers together, and all the variables

-3x^2-6x-(5x^2+30x+25)+45=0

We get rid of parentheses

-3x^2-5x^2-6x-30x-25+45=0

We add all the numbers together, and all the variables

-8x^2-36x+20=0

a = -8; b = -36; c = +20;
Δ = b2-4ac
Δ = -362-4·(-8)·20
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-44}{2*-8}=\frac{-8}{-16}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+44}{2*-8}=\frac{80}{-16}
=-5
$