6-5x+2*2x=4+2x(x-6)

Solution for 6-5x+2*2x=4+2x(x-6) equation:

6-5x+2*2x=4+2x(x-6)

We move all terms to the left:

6-5x+2*2x-(4+2x(x-6))=0

Wy multiply elements

-5x+4x-(4+2x(x-6))+6=0


We calculate terms in parentheses: -(4+2x(x-6)), so:

4+2x(x-6)

determiningTheFunctionDomain
2x(x-6)+4

We multiply parentheses

2x^2-12x+4

Back to the equation:

-(2x^2-12x+4)


We add all the numbers together, and all the variables

-1x-(2x^2-12x+4)+6=0

We get rid of parentheses

-2x^2-1x+12x-4+6=0

We add all the numbers together, and all the variables

-2x^2+11x+2=0

a = -2; b = 11; c = +2;
Δ = b2-4ac
Δ = 112-4·(-2)·2
Δ = 137
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{-(11)-\sqrt{137}}{2*-2}=\frac{-11-\sqrt{137}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{137}}{2*-2}=\frac{-11+\sqrt{137}}{-4}
$