3/4x-3/5x-7/10=2

Solution for 3/4x-3/5x-7/10=2 equation:

3/4x-3/5x-7/10=2

We move all terms to the left:

3/4x-3/5x-7/10-(2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


determiningTheFunctionDomain
3/4x-3/5x-2-7/10=0

We calculate fractions


(-700x^2)/200x^2+150x/200x^2+(-120x)/200x^2-2=0

We multiply all the terms by the denominator


(-700x^2)+150x+(-120x)-2*200x^2=0

Wy multiply elements

(-700x^2)-400x^2+150x+(-120x)=0

We get rid of parentheses

-700x^2-400x^2+150x-120x=0

We add all the numbers together, and all the variables

-1100x^2+30x=0

a = -1100; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-1100)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-1100}=\frac{-60}{-2200}
=3/110
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-1100}=\frac{0}{-2200}
=0
$