11/40y+1/8y=840

Solution for 11/40y+1/8y=840 equation:

11/40y+1/8y=840

We move all terms to the left:

11/40y+1/8y-(840)=0


Domain of the equation: 40y!=0

y!=0/40

y!=0

y∈R



Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We calculate fractions


88y/320y^2+40y/320y^2-840=0

We multiply all the terms by the denominator


88y+40y-840*320y^2=0

We add all the numbers together, and all the variables

128y-840*320y^2=0

Wy multiply elements

-268800y^2+128y=0

a = -268800; b = 128; c = 0;
Δ = b2-4ac
Δ = 1282-4·(-268800)·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-128}{2*-268800}=\frac{-256}{-537600}
=1/2100
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+128}{2*-268800}=\frac{0}{-537600}
=0
$