1*a*a/(2*a+2*a)=100

Solution for 1*a*a/(2*a+2*a)=100 equation:

1a*a/(2a+2a)=100

We move all terms to the left:

1a*a/(2a+2a)-(100)=0


Domain of the equation: (2a+2a)!=0

a∈R


We add all the numbers together, and all the variables

1a*a/(+4a)-100=0

We multiply all the terms by the denominator


1a*a-100*(+4a)=0

We multiply parentheses

1a*a-400a=0

Wy multiply elements

a^2-400a=0

a = 1; b = -400; c = 0;
Δ = b2-4ac
Δ = -4002-4·1·0
Δ = 160000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{160000}=400$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-400}{2*1}=\frac{0}{2}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+400}{2*1}=\frac{800}{2}
=400
$