5/8x+3/4=1/2x+7

Solution for 5/8x+3/4=1/2x+7 equation:

5/8x+3/4=1/2x+7

We move all terms to the left:

5/8x+3/4-(1/2x+7)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 2x+7)!=0

x∈R


We get rid of parentheses

5/8x-1/2x-7+3/4=0

We calculate fractions


96x^2/256x^2+160x/256x^2+(-128x)/256x^2-7=0

We multiply all the terms by the denominator


96x^2+160x+(-128x)-7*256x^2=0

Wy multiply elements

96x^2-1792x^2+160x+(-128x)=0

We get rid of parentheses

96x^2-1792x^2+160x-128x=0

We add all the numbers together, and all the variables

-1696x^2+32x=0

a = -1696; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-1696)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-1696}=\frac{-64}{-3392}
=1/53
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-1696}=\frac{0}{-3392}
=0
$