3/8x+3/4=7/2x-5

Solution for 3/8x+3/4=7/2x-5 equation:

3/8x+3/4=7/2x-5

We move all terms to the left:

3/8x+3/4-(7/2x-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-7/2x+5+3/4=0

We calculate fractions


96x^2/256x^2+96x/256x^2+(-896x)/256x^2+5=0

We multiply all the terms by the denominator


96x^2+96x+(-896x)+5*256x^2=0

Wy multiply elements

96x^2+1280x^2+96x+(-896x)=0

We get rid of parentheses

96x^2+1280x^2+96x-896x=0

We add all the numbers together, and all the variables

1376x^2-800x=0

a = 1376; b = -800; c = 0;
Δ = b2-4ac
Δ = -8002-4·1376·0
Δ = 640000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{640000}=800$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-800)-800}{2*1376}=\frac{0}{2752}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-800)+800}{2*1376}=\frac{1600}{2752}
=25/43
$