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

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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 $

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