6a^2+11a=52

Solution for 6a^2+11a=52 equation:

6a^2+11a=52

We move all terms to the left:

6a^2+11a-(52)=0

a = 6; b = 11; c = -52;
Δ = b2-4ac
Δ = 112-4·6·(-52)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-37}{2*6}=\frac{-48}{12}
=-4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+37}{2*6}=\frac{26}{12}
=2+1/6
$