6x^-5x^2-44x+15=0

Solution for 6x^-5x^2-44x+15=0 equation:

6x^-5x^2-44x+15=0

We add all the numbers together, and all the variables

-5x^2-38x+15=0

a = -5; b = -38; c = +15;
Δ = b2-4ac
Δ = -382-4·(-5)·15
Δ = 1744
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:

$\sqrt{\Delta}=\sqrt{1744}=\sqrt{16*109}=\sqrt{16}*\sqrt{109}=4\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-4\sqrt{109}}{2*-5}=\frac{38-4\sqrt{109}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+4\sqrt{109}}{2*-5}=\frac{38+4\sqrt{109}}{-10}
$