2x(1-x)-x(x+2)=2x^2-15

Solution for 2x(1-x)-x(x+2)=2x^2-15 equation:

2x(1-x)-x(x+2)=2x^2-15

We move all terms to the left:

2x(1-x)-x(x+2)-(2x^2-15)=0

We add all the numbers together, and all the variables

2x(-1x+1)-x(x+2)-(2x^2-15)=0

We multiply parentheses

-2x^2-x^2+2x-2x-(2x^2-15)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5x^2+15=0

a = -5; b = 0; c = +15;
Δ = b2-4ac
Δ = 02-4·(-5)·15
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*-5}=\frac{0-10\sqrt{3}}{-10}
=-\frac{10\sqrt{3}}{-10}
=-\frac{\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*-5}=\frac{0+10\sqrt{3}}{-10}
=\frac{10\sqrt{3}}{-10}
=\frac{\sqrt{3}}{-1}
$