3/4y+(300-y)=252.5

Solution for 3/4y+(300-y)=252.5 equation:

3/4y+(300-y)=252.5

We move all terms to the left:

3/4y+(300-y)-(252.5)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

3/4y+(-1y+300)-(252.5)=0

We add all the numbers together, and all the variables

3/4y+(-1y+300)-252.5=0

We get rid of parentheses

3/4y-1y+300-252.5=0

We multiply all the terms by the denominator


-1y*4y+300*4y-(252.5)*4y+3=0

We multiply parentheses

-1y*4y+300*4y-1010y+3=0

Wy multiply elements

-4y^2+1200y-1010y+3=0

We add all the numbers together, and all the variables

-4y^2+190y+3=0

a = -4; b = 190; c = +3;
Δ = b2-4ac
Δ = 1902-4·(-4)·3
Δ = 36148
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{36148}=\sqrt{4*9037}=\sqrt{4}*\sqrt{9037}=2\sqrt{9037}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(190)-2\sqrt{9037}}{2*-4}=\frac{-190-2\sqrt{9037}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(190)+2\sqrt{9037}}{2*-4}=\frac{-190+2\sqrt{9037}}{-8}
$