4x^2+12x-71=0

Solution for 4x^2+12x-71=0 equation:

4x^2+12x-71=0

a = 4; b = 12; c = -71;
Δ = b2-4ac
Δ = 122-4·4·(-71)
Δ = 1280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-16\sqrt{5}}{2*4}=\frac{-12-16\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+16\sqrt{5}}{2*4}=\frac{-12+16\sqrt{5}}{8}
$