3x^2+24x-103=0

Solution for 3x^2+24x-103=0 equation:

3x^2+24x-103=0

a = 3; b = 24; c = -103;
Δ = b2-4ac
Δ = 242-4·3·(-103)
Δ = 1812
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:

$\sqrt{\Delta}=\sqrt{1812}=\sqrt{4*453}=\sqrt{4}*\sqrt{453}=2\sqrt{453}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{453}}{2*3}=\frac{-24-2\sqrt{453}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{453}}{2*3}=\frac{-24+2\sqrt{453}}{6}
$