2y=130-170+2(40+2y)/2

Solution for 2y=130-170+2(40+2y)/2 equation:

2y=130-170+2(40+2y)/2

We move all terms to the left:

2y-(130-170+2(40+2y)/2)=0

We add all the numbers together, and all the variables

2y-(130-170+2(2y+40)/2)=0

We multiply all the terms by the denominator


2y*2)-(130+2(2y+40)-170=0

We multiply parentheses

2y*2)-(130+4y+80-170=0

Wy multiply elements

4y^2+4y+80-170=0

We add all the numbers together, and all the variables

4y^2+4y-90=0

a = 4; b = 4; c = -90;
Δ = b2-4ac
Δ = 42-4·4·(-90)
Δ = 1456
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:

$\sqrt{\Delta}=\sqrt{1456}=\sqrt{16*91}=\sqrt{16}*\sqrt{91}=4\sqrt{91}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{91}}{2*4}=\frac{-4-4\sqrt{91}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{91}}{2*4}=\frac{-4+4\sqrt{91}}{8}
$