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

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

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

We move all terms to the left:

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


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

2-2x(x-3)

determiningTheFunctionDomain
-2x(x-3)+2

We multiply parentheses

-2x^2+6x+2

Back to the equation:

-(-2x^2+6x+2)


We get rid of parentheses

2x^2-6x+5x-2-10=0

We add all the numbers together, and all the variables

2x^2-1x-12=0

a = 2; b = -1; c = -12;
Δ = b2-4ac
Δ = -12-4·2·(-12)
Δ = 97
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{-(-1)-\sqrt{97}}{2*2}=\frac{1-\sqrt{97}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{97}}{2*2}=\frac{1+\sqrt{97}}{4}
$