3x^2-46x+126=0

Solution for 3x^2-46x+126=0 equation:

3x^2-46x+126=0

a = 3; b = -46; c = +126;
Δ = b2-4ac
Δ = -462-4·3·126
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{151}}{2*3}=\frac{46-2\sqrt{151}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{151}}{2*3}=\frac{46+2\sqrt{151}}{6}
$