3a^2+15a=11

Solution for 3a^2+15a=11 equation:

3a^2+15a=11

We move all terms to the left:

3a^2+15a-(11)=0

a = 3; b = 15; c = -11;
Δ = b2-4ac
Δ = 152-4·3·(-11)
Δ = 357
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{357}}{2*3}=\frac{-15-\sqrt{357}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{357}}{2*3}=\frac{-15+\sqrt{357}}{6}
$