53x^2+96x-189=0

Solution for 53x^2+96x-189=0 equation:

53x^2+96x-189=0

a = 53; b = 96; c = -189;
Δ = b2-4ac
Δ = 962-4·53·(-189)
Δ = 49284
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49284}=222$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-222}{2*53}=\frac{-318}{106}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+222}{2*53}=\frac{126}{106}
=1+10/53
$