Y-(4-3y)*2y-(3+4y)=1/5

Solution for Y-(4-3y)*2y-(3+4y)=1/5 equation:

-(4-3Y)*2Y-(3+4Y)=1/5

We move all terms to the left:

-(4-3Y)*2Y-(3+4Y)-(1/5)=0

We add all the numbers together, and all the variables

-(-3Y+4)*2Y-(4Y+3)-(+1/5)=0

We multiply parentheses

6Y^2-8Y-(4Y+3)-(+1/5)=0

We get rid of parentheses

6Y^2-8Y-4Y-3-1/5=0

We multiply all the terms by the denominator


6Y^2*5-8Y*5-4Y*5-1-3*5=0

We add all the numbers together, and all the variables

6Y^2*5-8Y*5-4Y*5-16=0

Wy multiply elements

30Y^2-40Y-20Y-16=0

We add all the numbers together, and all the variables

30Y^2-60Y-16=0

a = 30; b = -60; c = -16;
Δ = b2-4ac
Δ = -602-4·30·(-16)
Δ = 5520
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:

$\sqrt{\Delta}=\sqrt{5520}=\sqrt{16*345}=\sqrt{16}*\sqrt{345}=4\sqrt{345}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{345}}{2*30}=\frac{60-4\sqrt{345}}{60}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{345}}{2*30}=\frac{60+4\sqrt{345}}{60}
$