-1/2w+8=7+3/4w

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

-1/2w+8=7+3/4w

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 4w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-4w)/8w^2+(-6w)/8w^2-7+8=0

We add all the numbers together, and all the variables

(-4w)/8w^2+(-6w)/8w^2+1=0

We multiply all the terms by the denominator


(-4w)+(-6w)+1*8w^2=0

Wy multiply elements

8w^2+(-4w)+(-6w)=0

We get rid of parentheses

8w^2-4w-6w=0

We add all the numbers together, and all the variables

8w^2-10w=0

a = 8; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·8·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*8}=\frac{0}{16}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*8}=\frac{20}{16}
=1+1/4
$