-y+(-5y+6)+(3/4)y=22

Solution for -y+(-5y+6)+(3/4)y=22 equation:

-y+(-5y+6)+(3/4)y=22

We move all terms to the left:

-y+(-5y+6)+(3/4)y-(22)=0


Domain of the equation: 4)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-y+(-5y+6)+(+3/4)y-22=0

We add all the numbers together, and all the variables

-1y+(-5y+6)+(+3/4)y-22=0

We multiply parentheses

3y^2-1y+(-5y+6)-22=0

We get rid of parentheses

3y^2-1y-5y+6-22=0

We add all the numbers together, and all the variables

3y^2-6y-16=0

a = 3; b = -6; c = -16;
Δ = b2-4ac
Δ = -62-4·3·(-16)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{57}}{2*3}=\frac{6-2\sqrt{57}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{57}}{2*3}=\frac{6+2\sqrt{57}}{6}
$