-212x^2+46x+7=0

Solution for -212x^2+46x+7=0 equation:

-212x^2+46x+7=0

a = -212; b = 46; c = +7;
Δ = b2-4ac
Δ = 462-4·(-212)·7
Δ = 8052
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:

$\sqrt{\Delta}=\sqrt{8052}=\sqrt{4*2013}=\sqrt{4}*\sqrt{2013}=2\sqrt{2013}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{2013}}{2*-212}=\frac{-46-2\sqrt{2013}}{-424}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{2013}}{2*-212}=\frac{-46+2\sqrt{2013}}{-424}
$