-6/5x-1/2-3/2x=-3/4

Solution for -6/5x-1/2-3/2x=-3/4 equation:

-6/5x-1/2-3/2x=-3/4

We move all terms to the left:

-6/5x-1/2-3/2x-(-3/4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-6/5x-3/2x-1/2+3/4=0

We calculate fractions


120x^2/160x^2+(-192x)/160x^2+(-240x)/160x^2+(-80x)/160x^2=0

We multiply all the terms by the denominator


120x^2+(-192x)+(-240x)+(-80x)=0

We get rid of parentheses

120x^2-192x-240x-80x=0

We add all the numbers together, and all the variables

120x^2-512x=0

a = 120; b = -512; c = 0;
Δ = b2-4ac
Δ = -5122-4·120·0
Δ = 262144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{262144}=512$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-512)-512}{2*120}=\frac{0}{240}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-512)+512}{2*120}=\frac{1024}{240}
=4+4/15
$