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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-112x^2)/512x^2+128x/512x^2+768x/512x^2=0

We multiply all the terms by the denominator


(-112x^2)+128x+768x=0

We add all the numbers together, and all the variables

(-112x^2)+896x=0

We get rid of parentheses

-112x^2+896x=0

a = -112; b = 896; c = 0;
Δ = b2-4ac
Δ = 8962-4·(-112)·0
Δ = 802816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{802816}=896$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(896)-896}{2*-112}=\frac{-1792}{-224}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(896)+896}{2*-112}=\frac{0}{-224}
=0
$