-210+110x-6x^2=0

Solution for -210+110x-6x^2=0 equation:

-210+110x-6x^2=0

a = -6; b = 110; c = -210;
Δ = b2-4ac
Δ = 1102-4·(-6)·(-210)
Δ = 7060
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:

$\sqrt{\Delta}=\sqrt{7060}=\sqrt{4*1765}=\sqrt{4}*\sqrt{1765}=2\sqrt{1765}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-2\sqrt{1765}}{2*-6}=\frac{-110-2\sqrt{1765}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+2\sqrt{1765}}{2*-6}=\frac{-110+2\sqrt{1765}}{-12}
$