5x(2x-1)=6-(2x-1)

Solution for 5x(2x-1)=6-(2x-1) equation:

5x(2x-1)=6-(2x-1)

We move all terms to the left:

5x(2x-1)-(6-(2x-1))=0

We multiply parentheses

10x^2-5x-(6-(2x-1))=0


We calculate terms in parentheses: -(6-(2x-1)), so:

6-(2x-1)

determiningTheFunctionDomain
-(2x-1)+6

We get rid of parentheses

-2x+1+6

We add all the numbers together, and all the variables

-2x+7

Back to the equation:

-(-2x+7)


We get rid of parentheses

10x^2-5x+2x-7=0

We add all the numbers together, and all the variables

10x^2-3x-7=0

a = 10; b = -3; c = -7;
Δ = b2-4ac
Δ = -32-4·10·(-7)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-17}{2*10}=\frac{-14}{20}
=-7/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+17}{2*10}=\frac{20}{20}
=1
$