6x^2+14x-46=0

Solution for 6x^2+14x-46=0 equation:

6x^2+14x-46=0

a = 6; b = 14; c = -46;
Δ = b2-4ac
Δ = 142-4·6·(-46)
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10\sqrt{13}}{2*6}=\frac{-14-10\sqrt{13}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10\sqrt{13}}{2*6}=\frac{-14+10\sqrt{13}}{12}
$