3x+4=1/5x+5

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

3x+4=1/5x+5

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

15x^2-25x+20x-1=0

We add all the numbers together, and all the variables

15x^2-5x-1=0

a = 15; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·15·(-1)
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*15}=\frac{5-\sqrt{85}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{85}}{2*15}=\frac{5+\sqrt{85}}{30}
$