x+4=3/5x+3

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

x+4=3/5x+3

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

x-3/5x-3+4=0

We multiply all the terms by the denominator


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

Wy multiply elements

5x^2-15x+20x-3=0

We add all the numbers together, and all the variables

5x^2+5x-3=0

a = 5; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·5·(-3)
Δ = 85
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{-(5)-\sqrt{85}}{2*5}=\frac{-5-\sqrt{85}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{85}}{2*5}=\frac{-5+\sqrt{85}}{10}
$