x=7/5x-3

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}
$