3x2-4x-253=0

Solution for 3x2-4x-253=0 equation:

3x^2-4x-253=0

a = 3; b = -4; c = -253;
Δ = b2-4ac
Δ = -42-4·3·(-253)
Δ = 3052
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:

$\sqrt{\Delta}=\sqrt{3052}=\sqrt{4*763}=\sqrt{4}*\sqrt{763}=2\sqrt{763}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{763}}{2*3}=\frac{4-2\sqrt{763}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{763}}{2*3}=\frac{4+2\sqrt{763}}{6}
$