3x2+78x+147=0

Solution for 3x2+78x+147=0 equation:

3x^2+78x+147=0

a = 3; b = 78; c = +147;
Δ = b2-4ac
Δ = 782-4·3·147
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-12\sqrt{30}}{2*3}=\frac{-78-12\sqrt{30}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+12\sqrt{30}}{2*3}=\frac{-78+12\sqrt{30}}{6}
$