3x^2-10x-65=0

Solution for 3x^2-10x-65=0 equation:

3x^2-10x-65=0

a = 3; b = -10; c = -65;
Δ = b2-4ac
Δ = -102-4·3·(-65)
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{55}}{2*3}=\frac{10-4\sqrt{55}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{55}}{2*3}=\frac{10+4\sqrt{55}}{6}
$