7b^2+10b-23=0

Solution for 7b^2+10b-23=0 equation:

7b^2+10b-23=0

a = 7; b = 10; c = -23;
Δ = b2-4ac
Δ = 102-4·7·(-23)
Δ = 744
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:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{186}}{2*7}=\frac{-10-2\sqrt{186}}{14}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{186}}{2*7}=\frac{-10+2\sqrt{186}}{14}
$