7-3/8x=1/2x-5

Solution for 7-3/8x=1/2x-5 equation:

7-3/8x=1/2x-5

We move all terms to the left:

7-3/8x-(1/2x-5)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 2x-5)!=0

x∈R


We get rid of parentheses

-3/8x-1/2x+5+7=0

We calculate fractions


(-6x)/16x^2+(-8x)/16x^2+5+7=0

We add all the numbers together, and all the variables

(-6x)/16x^2+(-8x)/16x^2+12=0

We multiply all the terms by the denominator


(-6x)+(-8x)+12*16x^2=0

Wy multiply elements

192x^2+(-6x)+(-8x)=0

We get rid of parentheses

192x^2-6x-8x=0

We add all the numbers together, and all the variables

192x^2-14x=0

a = 192; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·192·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*192}=\frac{0}{384}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*192}=\frac{28}{384}
=7/96
$