3x^2+6x-103=0

Solution for 3x^2+6x-103=0 equation:

3x^2+6x-103=0

a = 3; b = 6; c = -103;
Δ = b2-4ac
Δ = 62-4·3·(-103)
Δ = 1272
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:

$\sqrt{\Delta}=\sqrt{1272}=\sqrt{4*318}=\sqrt{4}*\sqrt{318}=2\sqrt{318}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{318}}{2*3}=\frac{-6-2\sqrt{318}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{318}}{2*3}=\frac{-6+2\sqrt{318}}{6}
$