3x^2-10x-82=0

Solution for 3x^2-10x-82=0 equation:

3x^2-10x-82=0

a = 3; b = -10; c = -82;
Δ = b2-4ac
Δ = -102-4·3·(-82)
Δ = 1084
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:

$\sqrt{\Delta}=\sqrt{1084}=\sqrt{4*271}=\sqrt{4}*\sqrt{271}=2\sqrt{271}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{271}}{2*3}=\frac{10-2\sqrt{271}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{271}}{2*3}=\frac{10+2\sqrt{271}}{6}
$