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

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

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

We move all terms to the left:

1/8x+1/2-(-3/2x+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

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

We calculate fractions


8x/64x^2+24x/64x^2+8x/64x^2-7=0

We multiply all the terms by the denominator


8x+24x+8x-7*64x^2=0

We add all the numbers together, and all the variables

40x-7*64x^2=0

Wy multiply elements

-448x^2+40x=0

a = -448; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·(-448)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*-448}=\frac{-80}{-896}
=5/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*-448}=\frac{0}{-896}
=0
$