-7u^2+12u+2=0

Solution for -7u^2+12u+2=0 equation:

-7u^2+12u+2=0

a = -7; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·(-7)·2
Δ = 200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-10\sqrt{2}}{2*-7}=\frac{-12-10\sqrt{2}}{-14}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+10\sqrt{2}}{2*-7}=\frac{-12+10\sqrt{2}}{-14}
$