14-1/8x=3/4x-21

Solution for 14-1/8x=3/4x-21 equation:

14-1/8x=3/4x-21

We move all terms to the left:

14-1/8x-(3/4x-21)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x-21)!=0

x∈R


We get rid of parentheses

-1/8x-3/4x+21+14=0

We calculate fractions


(-4x)/32x^2+(-24x)/32x^2+21+14=0

We add all the numbers together, and all the variables

(-4x)/32x^2+(-24x)/32x^2+35=0

We multiply all the terms by the denominator


(-4x)+(-24x)+35*32x^2=0

Wy multiply elements

1120x^2+(-4x)+(-24x)=0

We get rid of parentheses

1120x^2-4x-24x=0

We add all the numbers together, and all the variables

1120x^2-28x=0

a = 1120; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·1120·0
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*1120}=\frac{0}{2240}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*1120}=\frac{56}{2240}
=1/40
$