3/4x+9/10-4/5x=0

Solution for 3/4x+9/10-4/5x=0 equation:

3/4x+9/10-4/5x=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


We calculate fractions


900x^2/200x^2+150x/200x^2+(-160x)/200x^2=0

We multiply all the terms by the denominator


900x^2+150x+(-160x)=0

We get rid of parentheses

900x^2+150x-160x=0

We add all the numbers together, and all the variables

900x^2-10x=0

a = 900; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·900·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*900}=\frac{0}{1800}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*900}=\frac{20}{1800}
=1/90
$