3/5x+4x=18

Solution for 3/5x+4x=18 equation:

3/5x+4x=18

We move all terms to the left:

3/5x+4x-(18)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

4x+3/5x-18=0

We multiply all the terms by the denominator


4x*5x-18*5x+3=0

Wy multiply elements

20x^2-90x+3=0

a = 20; b = -90; c = +3;
Δ = b2-4ac
Δ = -902-4·20·3
Δ = 7860
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7860}=\sqrt{4*1965}=\sqrt{4}*\sqrt{1965}=2\sqrt{1965}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{1965}}{2*20}=\frac{90-2\sqrt{1965}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{1965}}{2*20}=\frac{90+2\sqrt{1965}}{40}
$