4x=1/5x+3

Solution for 4x=1/5x+3 equation:

4x=1/5x+3

We move all terms to the left:

4x-(1/5x+3)=0


Domain of the equation: 5x+3)!=0

x∈R


We get rid of parentheses

4x-1/5x-3=0

We multiply all the terms by the denominator


4x*5x-3*5x-1=0

Wy multiply elements

20x^2-15x-1=0

a = 20; b = -15; c = -1;
Δ = b2-4ac
Δ = -152-4·20·(-1)
Δ = 305
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{305}}{2*20}=\frac{15-\sqrt{305}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{305}}{2*20}=\frac{15+\sqrt{305}}{40}
$