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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(2-2x+10x(x-3)), so:

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

determiningTheFunctionDomain
-2x+10x(x-3)+2

We multiply parentheses

10x^2-2x-30x+2

We add all the numbers together, and all the variables

10x^2-32x+2

Back to the equation:

-(10x^2-32x+2)


We get rid of parentheses

-10x^2+5x+32x-2-10=0

We add all the numbers together, and all the variables

-10x^2+37x-12=0

a = -10; b = 37; c = -12;
Δ = b2-4ac
Δ = 372-4·(-10)·(-12)
Δ = 889
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{-(37)-\sqrt{889}}{2*-10}=\frac{-37-\sqrt{889}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{889}}{2*-10}=\frac{-37+\sqrt{889}}{-20}
$