3x^2-16x-157=0

Solution for 3x^2-16x-157=0 equation:

3x^2-16x-157=0

a = 3; b = -16; c = -157;
Δ = b2-4ac
Δ = -162-4·3·(-157)
Δ = 2140
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:

$\sqrt{\Delta}=\sqrt{2140}=\sqrt{4*535}=\sqrt{4}*\sqrt{535}=2\sqrt{535}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{535}}{2*3}=\frac{16-2\sqrt{535}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{535}}{2*3}=\frac{16+2\sqrt{535}}{6}
$