4/5x-18=1/10x+6

Solution for 4/5x-18=1/10x+6 equation:

4/5x-18=1/10x+6

We move all terms to the left:

4/5x-18-(1/10x+6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x+6)!=0

x∈R


We get rid of parentheses

4/5x-1/10x-6-18=0

We calculate fractions


40x/50x^2+(-5x)/50x^2-6-18=0

We add all the numbers together, and all the variables

40x/50x^2+(-5x)/50x^2-24=0

We multiply all the terms by the denominator


40x+(-5x)-24*50x^2=0

Wy multiply elements

-1200x^2+40x+(-5x)=0

We get rid of parentheses

-1200x^2+40x-5x=0

We add all the numbers together, and all the variables

-1200x^2+35x=0

a = -1200; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·(-1200)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*-1200}=\frac{-70}{-2400}
=7/240
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*-1200}=\frac{0}{-2400}
=0
$