3x^2-10x-182=0

Solution for 3x^2-10x-182=0 equation:

3x^2-10x-182=0

a = 3; b = -10; c = -182;
Δ = b2-4ac
Δ = -102-4·3·(-182)
Δ = 2284
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:

$\sqrt{\Delta}=\sqrt{2284}=\sqrt{4*571}=\sqrt{4}*\sqrt{571}=2\sqrt{571}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{571}}{2*3}=\frac{10-2\sqrt{571}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{571}}{2*3}=\frac{10+2\sqrt{571}}{6}
$