7b^2-14b-43=-6

Solution for 7b^2-14b-43=-6 equation:

7b^2-14b-43=-6

We move all terms to the left:

7b^2-14b-43-(-6)=0

We add all the numbers together, and all the variables

7b^2-14b-37=0

a = 7; b = -14; c = -37;
Δ = b2-4ac
Δ = -142-4·7·(-37)
Δ = 1232
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:

$\sqrt{\Delta}=\sqrt{1232}=\sqrt{16*77}=\sqrt{16}*\sqrt{77}=4\sqrt{77}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{77}}{2*7}=\frac{14-4\sqrt{77}}{14}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{77}}{2*7}=\frac{14+4\sqrt{77}}{14}
$