4b^2+4b-13=0

Solution for 4b^2+4b-13=0 equation:

4b^2+4b-13=0

a = 4; b = 4; c = -13;
Δ = b2-4ac
Δ = 42-4·4·(-13)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{14}}{2*4}=\frac{-4-4\sqrt{14}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{14}}{2*4}=\frac{-4+4\sqrt{14}}{8}
$