6x^2-10x+8=3x+6

Solution for 6x^2-10x+8=3x+6 equation:

6x^2-10x+8=3x+6

We move all terms to the left:

6x^2-10x+8-(3x+6)=0

We get rid of parentheses

6x^2-10x-3x-6+8=0

We add all the numbers together, and all the variables

6x^2-13x+2=0

a = 6; b = -13; c = +2;
Δ = b2-4ac
Δ = -132-4·6·2
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-11}{2*6}=\frac{2}{12}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+11}{2*6}=\frac{24}{12}
=2
$