6b^2+2b-67=7

Solution for 6b^2+2b-67=7 equation:

6b^2+2b-67=7

We move all terms to the left:

6b^2+2b-67-(7)=0

We add all the numbers together, and all the variables

6b^2+2b-74=0

a = 6; b = 2; c = -74;
Δ = b2-4ac
Δ = 22-4·6·(-74)
Δ = 1780
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:

$\sqrt{\Delta}=\sqrt{1780}=\sqrt{4*445}=\sqrt{4}*\sqrt{445}=2\sqrt{445}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{445}}{2*6}=\frac{-2-2\sqrt{445}}{12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{445}}{2*6}=\frac{-2+2\sqrt{445}}{12}
$