4a^2+2a-11=-4

Solution for 4a^2+2a-11=-4 equation:

4a^2+2a-11=-4

We move all terms to the left:

4a^2+2a-11-(-4)=0

We add all the numbers together, and all the variables

4a^2+2a-7=0

a = 4; b = 2; c = -7;
Δ = b2-4ac
Δ = 22-4·4·(-7)
Δ = 116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{29}}{2*4}=\frac{-2-2\sqrt{29}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{29}}{2*4}=\frac{-2+2\sqrt{29}}{8}
$