2x^2+17x^2+32x-15=0

Solution for 2x^2+17x^2+32x-15=0 equation:

2x^2+17x^2+32x-15=0

We add all the numbers together, and all the variables

19x^2+32x-15=0

a = 19; b = 32; c = -15;
Δ = b2-4ac
Δ = 322-4·19·(-15)
Δ = 2164
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:

$\sqrt{\Delta}=\sqrt{2164}=\sqrt{4*541}=\sqrt{4}*\sqrt{541}=2\sqrt{541}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{541}}{2*19}=\frac{-32-2\sqrt{541}}{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{541}}{2*19}=\frac{-32+2\sqrt{541}}{38}
$