6x^2-30x-35=0

Solution for 6x^2-30x-35=0 equation:

6x^2-30x-35=0

a = 6; b = -30; c = -35;
Δ = b2-4ac
Δ = -302-4·6·(-35)
Δ = 1740
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:

$\sqrt{\Delta}=\sqrt{1740}=\sqrt{4*435}=\sqrt{4}*\sqrt{435}=2\sqrt{435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{435}}{2*6}=\frac{30-2\sqrt{435}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{435}}{2*6}=\frac{30+2\sqrt{435}}{12}
$