2x^2+13x-189=0

Solution for 2x^2+13x-189=0 equation:

2x^2+13x-189=0

a = 2; b = 13; c = -189;
Δ = b2-4ac
Δ = 132-4·2·(-189)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-41}{2*2}=\frac{-54}{4}
=-13+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+41}{2*2}=\frac{28}{4}
=7
$