7/5x-4.1=6.74.5x

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Solution for 7/5x-4.1=6.74.5x equation: 



7/5x-4.1=6.74.5x

We move all terms to the left:

7/5x-4.1-(6.74.5x)=0



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



We add all the numbers together, and all the variables

7/5x-(+3.37x)-4.1=0

We get rid of parentheses

7/5x-3.37x-4.1=0

We multiply all the terms by the denominator


-(3.37x)*5x-(4.1)*5x+7=0

We add all the numbers together, and all the variables

-(+3.37x)*5x-(4.1)*5x+7=0

We multiply parentheses

-15x^2-20.5x+7=0

a = -15; b = -20.5; c = +7;
Δ = b2-4ac
Δ = -20.52-4·(-15)·7
Δ = 840.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20.5)-\sqrt{840.25}}{2*-15}=\frac{20.5-\sqrt{840.25}}{-30}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20.5)+\sqrt{840.25}}{2*-15}=\frac{20.5+\sqrt{840.25}}{-30}
$

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