6x^2+23x=-8

Solution for 6x^2+23x=-8 equation:

6x^2+23x=-8

We move all terms to the left:

6x^2+23x-(-8)=0

We add all the numbers together, and all the variables

6x^2+23x+8=0

a = 6; b = 23; c = +8;
Δ = b2-4ac
Δ = 232-4·6·8
Δ = 337
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{-(23)-\sqrt{337}}{2*6}=\frac{-23-\sqrt{337}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{337}}{2*6}=\frac{-23+\sqrt{337}}{12}
$