x.0.5(5-7x)=8-(4x+6)

Solution for x.0.5(5-7x)=8-(4x+6) equation:

x.0.5(5-7x)=8-(4x+6)

We move all terms to the left:

x.0.5(5-7x)-(8-(4x+6))=0

We add all the numbers together, and all the variables

x.0.5(-7x+5)-(8-(4x+6))=0

We multiply parentheses

-7x^2+5x-(8-(4x+6))=0


We calculate terms in parentheses: -(8-(4x+6)), so:

8-(4x+6)

determiningTheFunctionDomain
-(4x+6)+8

We get rid of parentheses

-4x-6+8

We add all the numbers together, and all the variables

-4x+2

Back to the equation:

-(-4x+2)


We get rid of parentheses

-7x^2+5x+4x-2=0

We add all the numbers together, and all the variables

-7x^2+9x-2=0

a = -7; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·(-7)·(-2)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-5}{2*-7}=\frac{-14}{-14}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+5}{2*-7}=\frac{-4}{-14}
=2/7
$