40/50a+90/100a=60

Solution for 40/50a+90/100a=60 equation:

40/50a+90/100a=60

We move all terms to the left:

40/50a+90/100a-(60)=0


Domain of the equation: 50a!=0

a!=0/50

a!=0

a∈R



Domain of the equation: 100a!=0

a!=0/100

a!=0

a∈R


We calculate fractions


4000a/5000a^2+4500a/5000a^2-60=0

We multiply all the terms by the denominator


4000a+4500a-60*5000a^2=0

We add all the numbers together, and all the variables

8500a-60*5000a^2=0

Wy multiply elements

-300000a^2+8500a=0

a = -300000; b = 8500; c = 0;
Δ = b2-4ac
Δ = 85002-4·(-300000)·0
Δ = 72250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{72250000}=8500$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8500)-8500}{2*-300000}=\frac{-17000}{-600000}
=17/600
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8500)+8500}{2*-300000}=\frac{0}{-600000}
=0
$