4x2+12x=91

Solution for 4x2+12x=91 equation:

4x^2+12x=91

We move all terms to the left:

4x^2+12x-(91)=0

a = 4; b = 12; c = -91;
Δ = b2-4ac
Δ = 122-4·4·(-91)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-40}{2*4}=\frac{-52}{8}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+40}{2*4}=\frac{28}{8}
=3+1/2
$