1/5w+6=-w+24

Solution for 1/5w+6=-w+24 equation:

1/5w+6=-w+24

We move all terms to the left:

1/5w+6-(-w+24)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R


We add all the numbers together, and all the variables

1/5w-(-1w+24)+6=0

We get rid of parentheses

1/5w+1w-24+6=0

We multiply all the terms by the denominator


1w*5w-24*5w+6*5w+1=0

Wy multiply elements

5w^2-120w+30w+1=0

We add all the numbers together, and all the variables

5w^2-90w+1=0

a = 5; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·5·1
Δ = 8080
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:

$\sqrt{\Delta}=\sqrt{8080}=\sqrt{16*505}=\sqrt{16}*\sqrt{505}=4\sqrt{505}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-4\sqrt{505}}{2*5}=\frac{90-4\sqrt{505}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+4\sqrt{505}}{2*5}=\frac{90+4\sqrt{505}}{10}
$