(2-x)(5x+1)-(3+x)(x-1)+8x^-15x+3=0

Solution for (2-x)(5x+1)-(3+x)(x-1)+8x^-15x+3=0 equation:

(2-x)(5x+1)-(3+x)(x-1)+8x^-15x+3=0

We add all the numbers together, and all the variables

(-1x+2)(5x+1)-(x+3)(x-1)+8x^-15x+3=0

We add all the numbers together, and all the variables

-7x+(-1x+2)(5x+1)-(x+3)(x-1)+3=0

We multiply parentheses ..

(-5x^2-1x+10x+2)-7x-(x+3)(x-1)+3=0

We get rid of parentheses

-5x^2-1x+10x-7x-(x+3)(x-1)+2+3=0

We multiply parentheses ..

-5x^2-(+x^2-1x+3x-3)-1x+10x-7x+2+3=0

We add all the numbers together, and all the variables

-5x^2-(+x^2-1x+3x-3)+2x+5=0

We get rid of parentheses

-5x^2-x^2+1x-3x+2x+3+5=0

We add all the numbers together, and all the variables

-6x^2+8=0

a = -6; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-6)·8
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*-6}=\frac{0-8\sqrt{3}}{-12}
=-\frac{8\sqrt{3}}{-12}
=-\frac{2\sqrt{3}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*-6}=\frac{0+8\sqrt{3}}{-12}
=\frac{8\sqrt{3}}{-12}
=\frac{2\sqrt{3}}{-3}
$