3x^2-74x+312=0

Solution for 3x^2-74x+312=0 equation:

3x^2-74x+312=0

a = 3; b = -74; c = +312;
Δ = b2-4ac
Δ = -742-4·3·312
Δ = 1732
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:

$\sqrt{\Delta}=\sqrt{1732}=\sqrt{4*433}=\sqrt{4}*\sqrt{433}=2\sqrt{433}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-2\sqrt{433}}{2*3}=\frac{74-2\sqrt{433}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+2\sqrt{433}}{2*3}=\frac{74+2\sqrt{433}}{6}
$