x=2.5/5x+3.75

Solution for x=2.5/5x+3.75 equation:

x=2.5/5x+3.75

We move all terms to the left:

x-(2.5/5x+3.75)=0


Domain of the equation: 5x+3.75)!=0

x∈R


We get rid of parentheses

x-2.5/5x-3.75=0

We multiply all the terms by the denominator


x*5x-(3.75)*5x-2.5=0

We multiply parentheses

x*5x-18.75x-2.5=0

Wy multiply elements

5x^2-18.75x-2.5=0

a = 5; b = -18.75; c = -2.5;
Δ = b2-4ac
Δ = -18.752-4·5·(-2.5)
Δ = 401.5625
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{-(-18.75)-\sqrt{401.5625}}{2*5}=\frac{18.75-\sqrt{401.5625}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18.75)+\sqrt{401.5625}}{2*5}=\frac{18.75+\sqrt{401.5625}}{10}
$