45x2-32x-80=0

Solution for 45x2-32x-80=0 equation:

45x^2-32x-80=0

a = 45; b = -32; c = -80;
Δ = b2-4ac
Δ = -322-4·45·(-80)
Δ = 15424
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:

$\sqrt{\Delta}=\sqrt{15424}=\sqrt{64*241}=\sqrt{64}*\sqrt{241}=8\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{241}}{2*45}=\frac{32-8\sqrt{241}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{241}}{2*45}=\frac{32+8\sqrt{241}}{90}
$