1.5(6x-3)7x=3-(7-x)

Solution for 1.5(6x-3)7x=3-(7-x) equation:

1.5(6x-3)7x=3-(7-x)

We move all terms to the left:

1.5(6x-3)7x-(3-(7-x))=0

We add all the numbers together, and all the variables

1.5(6x-3)7x-(3-(-1x+7))=0

We multiply parentheses

60x^2-30x-(3-(-1x+7))=0


We calculate terms in parentheses: -(3-(-1x+7)), so:

3-(-1x+7)

determiningTheFunctionDomain
-(-1x+7)+3

We get rid of parentheses

1x-7+3

We add all the numbers together, and all the variables

x-4

Back to the equation:

-(x-4)


We get rid of parentheses

60x^2-30x-x+4=0

We add all the numbers together, and all the variables

60x^2-31x+4=0

a = 60; b = -31; c = +4;
Δ = b2-4ac
Δ = -312-4·60·4
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-1}{2*60}=\frac{30}{120}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+1}{2*60}=\frac{32}{120}
=4/15
$