6x2+12x=71

Solution for 6x2+12x=71 equation:

6x^2+12x=71

We move all terms to the left:

6x^2+12x-(71)=0

a = 6; b = 12; c = -71;
Δ = b2-4ac
Δ = 122-4·6·(-71)
Δ = 1848
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:

$\sqrt{\Delta}=\sqrt{1848}=\sqrt{4*462}=\sqrt{4}*\sqrt{462}=2\sqrt{462}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{462}}{2*6}=\frac{-12-2\sqrt{462}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{462}}{2*6}=\frac{-12+2\sqrt{462}}{12}
$