3x^2+26x-153=0

Solution for 3x^2+26x-153=0 equation:

3x^2+26x-153=0

a = 3; b = 26; c = -153;
Δ = b2-4ac
Δ = 262-4·3·(-153)
Δ = 2512
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:

$\sqrt{\Delta}=\sqrt{2512}=\sqrt{16*157}=\sqrt{16}*\sqrt{157}=4\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-4\sqrt{157}}{2*3}=\frac{-26-4\sqrt{157}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+4\sqrt{157}}{2*3}=\frac{-26+4\sqrt{157}}{6}
$