-6x^2+68x-94=0

Solution for -6x^2+68x-94=0 equation:

-6x^2+68x-94=0

a = -6; b = 68; c = -94;
Δ = b2-4ac
Δ = 682-4·(-6)·(-94)
Δ = 2368
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:

$\sqrt{\Delta}=\sqrt{2368}=\sqrt{64*37}=\sqrt{64}*\sqrt{37}=8\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-8\sqrt{37}}{2*-6}=\frac{-68-8\sqrt{37}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+8\sqrt{37}}{2*-6}=\frac{-68+8\sqrt{37}}{-12}
$