2(x-1)(x+2)=5x^-6x

Solution for 2(x-1)(x+2)=5x^-6x equation:

2(x-1)(x+2)=5x^-6x

We move all terms to the left:

2(x-1)(x+2)-(5x^-6x)=0

We get rid of parentheses

2(x-1)(x+2)-5x^+6x=0

We multiply parentheses ..

2(+x^2+2x-1x-2)-5x^+6x=0

We add all the numbers together, and all the variables

2(+x^2+2x-1x-2)+x=0

We multiply parentheses

2x^2+4x-2x+x-4=0

We add all the numbers together, and all the variables

2x^2+3x-4=0

a = 2; b = 3; c = -4;
Δ = b2-4ac
Δ = 32-4·2·(-4)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{41}}{2*2}=\frac{-3-\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{41}}{2*2}=\frac{-3+\sqrt{41}}{4}
$