7/10x-18=51/5x

Solution for 7/10x-18=51/5x equation:

7/10x-18=51/5x

We move all terms to the left:

7/10x-18-(51/5x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7/10x-(+51/5x)-18=0

We get rid of parentheses

7/10x-51/5x-18=0

We calculate fractions


35x/50x^2+(-510x)/50x^2-18=0

We multiply all the terms by the denominator


35x+(-510x)-18*50x^2=0

Wy multiply elements

-900x^2+35x+(-510x)=0

We get rid of parentheses

-900x^2+35x-510x=0

We add all the numbers together, and all the variables

-900x^2-475x=0

a = -900; b = -475; c = 0;
Δ = b2-4ac
Δ = -4752-4·(-900)·0
Δ = 225625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225625}=475$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-475)-475}{2*-900}=\frac{0}{-1800}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-475)+475}{2*-900}=\frac{950}{-1800}
=-19/36
$