x^2+13x-32/6=0

Solution for x^2+13x-32/6=0 equation:

x^2+13x-32/6=0

We multiply all the terms by the denominator


x^2*6+13x*6-32=0

Wy multiply elements

6x^2+78x-32=0

a = 6; b = 78; c = -32;
Δ = b2-4ac
Δ = 782-4·6·(-32)
Δ = 6852
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:

$\sqrt{\Delta}=\sqrt{6852}=\sqrt{4*1713}=\sqrt{4}*\sqrt{1713}=2\sqrt{1713}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{1713}}{2*6}=\frac{-78-2\sqrt{1713}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{1713}}{2*6}=\frac{-78+2\sqrt{1713}}{12}
$