7/10x-18=26/5x

Solution for 7/10x-18=26/5x equation:

7/10x-18=26/5x

We move all terms to the left:

7/10x-18-(26/5x)=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-(+26/5x)-18=0

We get rid of parentheses

7/10x-26/5x-18=0

We calculate fractions


35x/50x^2+(-260x)/50x^2-18=0

We multiply all the terms by the denominator


35x+(-260x)-18*50x^2=0

Wy multiply elements

-900x^2+35x+(-260x)=0

We get rid of parentheses

-900x^2+35x-260x=0

We add all the numbers together, and all the variables

-900x^2-225x=0

a = -900; b = -225; c = 0;
Δ = b2-4ac
Δ = -2252-4·(-900)·0
Δ = 50625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{50625}=225$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-225)-225}{2*-900}=\frac{0}{-1800}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-225)+225}{2*-900}=\frac{450}{-1800}
=-1/4
$