6b^2+2b-19=-4

Solution for 6b^2+2b-19=-4 equation:

6b^2+2b-19=-4

We move all terms to the left:

6b^2+2b-19-(-4)=0

We add all the numbers together, and all the variables

6b^2+2b-15=0

a = 6; b = 2; c = -15;
Δ = b2-4ac
Δ = 22-4·6·(-15)
Δ = 364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{91}}{2*6}=\frac{-2-2\sqrt{91}}{12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{91}}{2*6}=\frac{-2+2\sqrt{91}}{12}
$