120-y-1/4y=90

Solution for 120-y-1/4y=90 equation:

120-y-1/4y=90

We move all terms to the left:

120-y-1/4y-(90)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

-1y-1/4y+30=0

We multiply all the terms by the denominator


-1y*4y+30*4y-1=0

Wy multiply elements

-4y^2+120y-1=0

a = -4; b = 120; c = -1;
Δ = b2-4ac
Δ = 1202-4·(-4)·(-1)
Δ = 14384
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:

$\sqrt{\Delta}=\sqrt{14384}=\sqrt{16*899}=\sqrt{16}*\sqrt{899}=4\sqrt{899}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-4\sqrt{899}}{2*-4}=\frac{-120-4\sqrt{899}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+4\sqrt{899}}{2*-4}=\frac{-120+4\sqrt{899}}{-8}
$