34b(b+8)=15

Solution for 34b(b+8)=15 equation:

34b(b+8)=15

We move all terms to the left:

34b(b+8)-(15)=0

We multiply parentheses

34b^2+272b-15=0

a = 34; b = 272; c = -15;
Δ = b2-4ac
Δ = 2722-4·34·(-15)
Δ = 76024
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:

$\sqrt{\Delta}=\sqrt{76024}=\sqrt{4*19006}=\sqrt{4}*\sqrt{19006}=2\sqrt{19006}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(272)-2\sqrt{19006}}{2*34}=\frac{-272-2\sqrt{19006}}{68}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(272)+2\sqrt{19006}}{2*34}=\frac{-272+2\sqrt{19006}}{68}
$