-2x^2+14x+12=0

Solution for -2x^2+14x+12=0 equation:

-2x^2+14x+12=0

a = -2; b = 14; c = +12;
Δ = b2-4ac
Δ = 142-4·(-2)·12
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{73}}{2*-2}=\frac{-14-2\sqrt{73}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{73}}{2*-2}=\frac{-14+2\sqrt{73}}{-4}
$