6x^2+28x-89=0

Solution for 6x^2+28x-89=0 equation:

6x^2+28x-89=0

a = 6; b = 28; c = -89;
Δ = b2-4ac
Δ = 282-4·6·(-89)
Δ = 2920
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:

$\sqrt{\Delta}=\sqrt{2920}=\sqrt{4*730}=\sqrt{4}*\sqrt{730}=2\sqrt{730}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{730}}{2*6}=\frac{-28-2\sqrt{730}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{730}}{2*6}=\frac{-28+2\sqrt{730}}{12}
$