3x^2+5x-15=17-15x

Solution for 3x^2+5x-15=17-15x equation:

3x^2+5x-15=17-15x

We move all terms to the left:

3x^2+5x-15-(17-15x)=0

We add all the numbers together, and all the variables

3x^2+5x-(-15x+17)-15=0

We get rid of parentheses

3x^2+5x+15x-17-15=0

We add all the numbers together, and all the variables

3x^2+20x-32=0

a = 3; b = 20; c = -32;
Δ = b2-4ac
Δ = 202-4·3·(-32)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-28}{2*3}=\frac{-48}{6}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+28}{2*3}=\frac{8}{6}
=1+1/3
$