15b^2=34b+12=-3

Solution for 15b^2=34b+12=-3 equation:

15b^2=34b+12=-3

We move all terms to the left:

15b^2-(34b+12)=0

We get rid of parentheses

15b^2-34b-12=0

a = 15; b = -34; c = -12;
Δ = b2-4ac
Δ = -342-4·15·(-12)
Δ = 1876
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:

$\sqrt{\Delta}=\sqrt{1876}=\sqrt{4*469}=\sqrt{4}*\sqrt{469}=2\sqrt{469}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{469}}{2*15}=\frac{34-2\sqrt{469}}{30}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{469}}{2*15}=\frac{34+2\sqrt{469}}{30}
$