1/2(x)+1+3/8(x)=7

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

1/2(x)+1+3/8(x)=7

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+3/8x-6=0

We calculate fractions


8x/16x^2+6x/16x^2-6=0

We multiply all the terms by the denominator


8x+6x-6*16x^2=0

We add all the numbers together, and all the variables

14x-6*16x^2=0

Wy multiply elements

-96x^2+14x=0

a = -96; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-96)·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*-96}=\frac{-28}{-192}
=7/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-96}=\frac{0}{-192}
=0
$