x=7/5x-3

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Solution for x=7/5x-3 equation:



x=7/5x-3
We move all terms to the left:
x-(7/5x-3)=0
Domain of the equation: 5x-3)!=0
x∈R
We get rid of parentheses
x-7/5x+3=0
We multiply all the terms by the denominator
x*5x+3*5x-7=0
Wy multiply elements
5x^2+15x-7=0
a = 5; b = 15; c = -7;
Δ = b2-4ac
Δ = 152-4·5·(-7)
Δ = 365
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{-(15)-\sqrt{365}}{2*5}=\frac{-15-\sqrt{365}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{365}}{2*5}=\frac{-15+\sqrt{365}}{10} $

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