-73/4x=1/2x-3

Solution for -73/4x=1/2x-3 equation:

-73/4x=1/2x-3

We move all terms to the left:

-73/4x-(1/2x-3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

-73/4x-1/2x+3=0

We calculate fractions


(-146x)/8x^2+(-4x)/8x^2+3=0

We multiply all the terms by the denominator


(-146x)+(-4x)+3*8x^2=0

Wy multiply elements

24x^2+(-146x)+(-4x)=0

We get rid of parentheses

24x^2-146x-4x=0

We add all the numbers together, and all the variables

24x^2-150x=0

a = 24; b = -150; c = 0;
Δ = b2-4ac
Δ = -1502-4·24·0
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-150}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+150}{2*24}=\frac{300}{48}
=6+1/4
$