6x+8=3x^2+7x-1

Solution for 6x+8=3x^2+7x-1 equation:

6x+8=3x^2+7x-1

We move all terms to the left:

6x+8-(3x^2+7x-1)=0

We get rid of parentheses

-3x^2+6x-7x+1+8=0

We add all the numbers together, and all the variables

-3x^2-1x+9=0

a = -3; b = -1; c = +9;
Δ = b2-4ac
Δ = -12-4·(-3)·9
Δ = 109
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{109}}{2*-3}=\frac{1-\sqrt{109}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{109}}{2*-3}=\frac{1+\sqrt{109}}{-6}
$