X + y = 5.90
2x + 4y = 16.80

2+4y(5.90-y)=16.80

We move all terms to the left:

2+4y(5.90-y)-(16.80)=0

We add all the numbers together, and all the variables

4y(-1y+5.9)+2-(16.8)=0

We add all the numbers together, and all the variables

4y(-1y+5.9)-14.8=0

We multiply parentheses

-4y^2+23.6y-14.8=0

a = -4; b = 23.6; c = -14.8;
Δ = b2-4ac
Δ = 23.62-4·(-4)·(-14.8)
Δ = 320.16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
y1=−b−Δ√2ay2=−b+Δ√2a

y1=−b−Δ√2a=−(23.6)−320.16√2∗−4=−23.6−320.16√−8

y2=−b+Δ√2a=−(23.6)+320.16√2∗−4=−23.6+320.16√−8