-6x(x-2)=7-(5-2x)

Solution for -6x(x-2)=7-(5-2x) equation:

-6x(x-2)=7-(5-2x)

We move all terms to the left:

-6x(x-2)-(7-(5-2x))=0

We add all the numbers together, and all the variables

-6x(x-2)-(7-(-2x+5))=0

We multiply parentheses

-6x^2+12x-(7-(-2x+5))=0


We calculate terms in parentheses: -(7-(-2x+5)), so:

7-(-2x+5)

determiningTheFunctionDomain
-(-2x+5)+7

We get rid of parentheses

2x-5+7

We add all the numbers together, and all the variables

2x+2

Back to the equation:

-(2x+2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -6; b = 10; c = -2;
Δ = b2-4ac
Δ = 102-4·(-6)·(-2)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{13}}{2*-6}=\frac{-10-2\sqrt{13}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{13}}{2*-6}=\frac{-10+2\sqrt{13}}{-12}
$