3x^2-4x+2=6x+15

Solution for 3x^2-4x+2=6x+15 equation:

3x^2-4x+2=6x+15

We move all terms to the left:

3x^2-4x+2-(6x+15)=0

We get rid of parentheses

3x^2-4x-6x-15+2=0

We add all the numbers together, and all the variables

3x^2-10x-13=0

a = 3; b = -10; c = -13;
Δ = b2-4ac
Δ = -102-4·3·(-13)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-16}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+16}{2*3}=\frac{26}{6}
=4+1/3
$