(x^2)-6x+9=(-5x^2)+20x-15

Solution for (x^2)-6x+9=(-5x^2)+20x-15 equation:

(x^2)-6x+9=(-5x^2)+20x-15

We move all terms to the left:

(x^2)-6x+9-((-5x^2)+20x-15)=0

We add all the numbers together, and all the variables

x^2-((-5x^2)+20x-15)-6x+9=0


We calculate terms in parentheses: -((-5x^2)+20x-15), so:

(-5x^2)+20x-15

We get rid of parentheses

-5x^2+20x-15

Back to the equation:

-(-5x^2+20x-15)


We get rid of parentheses

x^2+5x^2-20x-6x+15+9=0

We add all the numbers together, and all the variables

6x^2-26x+24=0

a = 6; b = -26; c = +24;
Δ = b2-4ac
Δ = -262-4·6·24
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-10}{2*6}=\frac{16}{12}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+10}{2*6}=\frac{36}{12}
=3
$