2(10)(4+1/2w)=(5+1/10w-30)(10)2

Solution for 2(10)(4+1/2w)=(5+1/10w-30)(10)2 equation:

2(10)(4+1/2w)=(5+1/10w-30)(10)2

We move all terms to the left:

2(10)(4+1/2w)-((5+1/10w-30)(10)2)=0


Domain of the equation: 2w)!=0

w!=0/1

w!=0

w∈R



Domain of the equation: 10w-30)102)!=0

w∈R


We add all the numbers together, and all the variables

210(1/2w+4)-((1/10w-25)102)=0

We multiply parentheses

210w-((1/10w-25)102)+840=0

We multiply all the terms by the denominator


210w*10w+840*10w-25)102)-((1-25)102)=0

We add all the numbers together, and all the variables

210w*10w+840*10w-25)102)-((-24)102)=0

We add all the numbers together, and all the variables

210w*10w+840*10w=0

Wy multiply elements

2100w^2+8400w=0

a = 2100; b = 8400; c = 0;
Δ = b2-4ac
Δ = 84002-4·2100·0
Δ = 70560000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{70560000}=8400$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8400)-8400}{2*2100}=\frac{-16800}{4200}
=-4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8400)+8400}{2*2100}=\frac{0}{4200}
=0
$