6a^2+11a-25=-3

Solution for 6a^2+11a-25=-3 equation:

6a^2+11a-25=-3

We move all terms to the left:

6a^2+11a-25-(-3)=0

We add all the numbers together, and all the variables

6a^2+11a-22=0

a = 6; b = 11; c = -22;
Δ = b2-4ac
Δ = 112-4·6·(-22)
Δ = 649
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{-(11)-\sqrt{649}}{2*6}=\frac{-11-\sqrt{649}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{649}}{2*6}=\frac{-11+\sqrt{649}}{12}
$