3x^2-12x-53=0

Solution for 3x^2-12x-53=0 equation:

3x^2-12x-53=0

a = 3; b = -12; c = -53;
Δ = b2-4ac
Δ = -122-4·3·(-53)
Δ = 780
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:

$\sqrt{\Delta}=\sqrt{780}=\sqrt{4*195}=\sqrt{4}*\sqrt{195}=2\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{195}}{2*3}=\frac{12-2\sqrt{195}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{195}}{2*3}=\frac{12+2\sqrt{195}}{6}
$