7/4y-y=15

Solution for 7/4y-y=15 equation:

7/4y-y=15

We move all terms to the left:

7/4y-y-(15)=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+7/4y-15=0

We multiply all the terms by the denominator


-1y*4y-15*4y+7=0

Wy multiply elements

-4y^2-60y+7=0

a = -4; b = -60; c = +7;
Δ = b2-4ac
Δ = -602-4·(-4)·7
Δ = 3712
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:

$\sqrt{\Delta}=\sqrt{3712}=\sqrt{64*58}=\sqrt{64}*\sqrt{58}=8\sqrt{58}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-8\sqrt{58}}{2*-4}=\frac{60-8\sqrt{58}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+8\sqrt{58}}{2*-4}=\frac{60+8\sqrt{58}}{-8}
$