14-1/8w=0.75w-21

Solution for 14-1/8w=0.75w-21 equation:

14-1/8w=0.75w-21

We move all terms to the left:

14-1/8w-(0.75w-21)=0


Domain of the equation: 8w!=0

w!=0/8

w!=0

w∈R


We get rid of parentheses

-1/8w-0.75w+21+14=0

We multiply all the terms by the denominator


-(0.75w)*8w+21*8w+14*8w-1=0

We add all the numbers together, and all the variables

-(+0.75w)*8w+21*8w+14*8w-1=0

We multiply parentheses

-0w^2+21*8w+14*8w-1=0

Wy multiply elements

-0w^2+168w+112w-1=0

We add all the numbers together, and all the variables

-1w^2+280w-1=0

a = -1; b = 280; c = -1;
Δ = b2-4ac
Δ = 2802-4·(-1)·(-1)
Δ = 78396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{78396}=\sqrt{4*19599}=\sqrt{4}*\sqrt{19599}=2\sqrt{19599}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-2\sqrt{19599}}{2*-1}=\frac{-280-2\sqrt{19599}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+2\sqrt{19599}}{2*-1}=\frac{-280+2\sqrt{19599}}{-2}
$