27x^2-10x-35=0

Solution for 27x^2-10x-35=0 equation:

27x^2-10x-35=0

a = 27; b = -10; c = -35;
Δ = b2-4ac
Δ = -102-4·27·(-35)
Δ = 3880
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:

$\sqrt{\Delta}=\sqrt{3880}=\sqrt{4*970}=\sqrt{4}*\sqrt{970}=2\sqrt{970}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{970}}{2*27}=\frac{10-2\sqrt{970}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{970}}{2*27}=\frac{10+2\sqrt{970}}{54}
$