5/16y+3/8y=2+1/4

Solution for 5/16y+3/8y=2+1/4 equation:

5/16y+3/8y=2+1/4

We move all terms to the left:

5/16y+3/8y-(2+1/4)=0


Domain of the equation: 16y!=0

y!=0/16

y!=0

y∈R



Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We add all the numbers together, and all the variables

5/16y+3/8y-(1/4+2)=0

We get rid of parentheses

5/16y+3/8y-2-1/4=0

We calculate fractions


(-1024y^2)/2048y^2+640y/2048y^2+768y/2048y^2-2=0

We multiply all the terms by the denominator


(-1024y^2)+640y+768y-2*2048y^2=0

We add all the numbers together, and all the variables

(-1024y^2)+1408y-2*2048y^2=0

Wy multiply elements

(-1024y^2)-4096y^2+1408y=0

We get rid of parentheses

-1024y^2-4096y^2+1408y=0

We add all the numbers together, and all the variables

-5120y^2+1408y=0

a = -5120; b = 1408; c = 0;
Δ = b2-4ac
Δ = 14082-4·(-5120)·0
Δ = 1982464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1982464}=1408$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1408)-1408}{2*-5120}=\frac{-2816}{-10240}
=11/40
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1408)+1408}{2*-5120}=\frac{0}{-10240}
=0
$