x^2+6x-3x^2+7x+6=8

Solution for x^2+6x-3x^2+7x+6=8 equation:

x^2+6x-3x^2+7x+6=8

We move all terms to the left:

x^2+6x-3x^2+7x+6-(8)=0

We add all the numbers together, and all the variables

-2x^2+13x-2=0

a = -2; b = 13; c = -2;
Δ = b2-4ac
Δ = 132-4·(-2)·(-2)
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3\sqrt{17}}{2*-2}=\frac{-13-3\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3\sqrt{17}}{2*-2}=\frac{-13+3\sqrt{17}}{-4}
$