-1/4x+7=5/8x

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

-1/4x+7=5/8x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-8x)/32x^2+(-20x)/32x^2+7=0

We multiply all the terms by the denominator


(-8x)+(-20x)+7*32x^2=0

Wy multiply elements

224x^2+(-8x)+(-20x)=0

We get rid of parentheses

224x^2-8x-20x=0

We add all the numbers together, and all the variables

224x^2-28x=0

a = 224; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·224·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-28}{2*224}=\frac{0}{448}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*224}=\frac{56}{448}
=1/8
$