3x^2-53x-140=0

Solution for 3x^2-53x-140=0 equation:

3x^2-53x-140=0

a = 3; b = -53; c = -140;
Δ = b2-4ac
Δ = -532-4·3·(-140)
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-67}{2*3}=\frac{-14}{6}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+67}{2*3}=\frac{120}{6}
=20
$