(x-10)-(-3x+5)x=2

Solution for (x-10)-(-3x+5)x=2 equation:

(x-10)-(-3x+5)x=2

We move all terms to the left:

(x-10)-(-3x+5)x-(2)=0

We multiply parentheses

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

We get rid of parentheses

3x^2+x-5x-10-2=0

We add all the numbers together, and all the variables

3x^2-4x-12=0

a = 3; b = -4; c = -12;
Δ = b2-4ac
Δ = -42-4·3·(-12)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{10}}{2*3}=\frac{4-4\sqrt{10}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{10}}{2*3}=\frac{4+4\sqrt{10}}{6}
$