-3/4x+6/5x=27/40

Solution for -3/4x+6/5x=27/40 equation:

-3/4x+6/5x=27/40

We move all terms to the left:

-3/4x+6/5x-(27/40)=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 add all the numbers together, and all the variables

-3/4x+6/5x-(+27/40)=0

We get rid of parentheses

-3/4x+6/5x-27/40=0

We calculate fractions


(-2700x^2)/3200x^2+(-2400x)/3200x^2+3840x/3200x^2=0

We multiply all the terms by the denominator


(-2700x^2)+(-2400x)+3840x=0

We add all the numbers together, and all the variables

(-2700x^2)+3840x+(-2400x)=0

We get rid of parentheses

-2700x^2+3840x-2400x=0

We add all the numbers together, and all the variables

-2700x^2+1440x=0

a = -2700; b = 1440; c = 0;
Δ = b2-4ac
Δ = 14402-4·(-2700)·0
Δ = 2073600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2073600}=1440$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1440)-1440}{2*-2700}=\frac{-2880}{-5400}
=8/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1440)+1440}{2*-2700}=\frac{0}{-5400}
=0
$