b2+14b-100=7

Solution for b2+14b-100=7 equation:

b2+14b-100=7

We move all terms to the left:

b2+14b-100-(7)=0

We add all the numbers together, and all the variables

b^2+14b-107=0

a = 1; b = 14; c = -107;
Δ = b2-4ac
Δ = 142-4·1·(-107)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{39}}{2*1}=\frac{-14-4\sqrt{39}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{39}}{2*1}=\frac{-14+4\sqrt{39}}{2}
$