y=-1/4(2y)+20

Solution for y=-1/4(2y)+20 equation:

y=-1/4(2y)+20

We move all terms to the left:

y-(-1/4(2y)+20)=0


Domain of the equation: 42y+20)!=0

y∈R


We get rid of parentheses

y+1/42y-20=0

We multiply all the terms by the denominator


y*42y-20*42y+1=0

Wy multiply elements

42y^2-840y+1=0

a = 42; b = -840; c = +1;
Δ = b2-4ac
Δ = -8402-4·42·1
Δ = 705432
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:

$\sqrt{\Delta}=\sqrt{705432}=\sqrt{4*176358}=\sqrt{4}*\sqrt{176358}=2\sqrt{176358}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-840)-2\sqrt{176358}}{2*42}=\frac{840-2\sqrt{176358}}{84}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-840)+2\sqrt{176358}}{2*42}=\frac{840+2\sqrt{176358}}{84}
$