30/100a=a-140

Solution for 30/100a=a-140 equation:

30/100a=a-140

We move all terms to the left:

30/100a-(a-140)=0


Domain of the equation: 100a!=0

a!=0/100

a!=0

a∈R


We get rid of parentheses

30/100a-a+140=0

We multiply all the terms by the denominator


-a*100a+140*100a+30=0

Wy multiply elements

-100a^2+14000a+30=0

a = -100; b = 14000; c = +30;
Δ = b2-4ac
Δ = 140002-4·(-100)·30
Δ = 196012000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{196012000}=\sqrt{400*490030}=\sqrt{400}*\sqrt{490030}=20\sqrt{490030}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14000)-20\sqrt{490030}}{2*-100}=\frac{-14000-20\sqrt{490030}}{-200}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14000)+20\sqrt{490030}}{2*-100}=\frac{-14000+20\sqrt{490030}}{-200}
$