(1/2)(4-14y)=y+50

Solution for (1/2)(4-14y)=y+50 equation:

(1/2)(4-14y)=y+50

We move all terms to the left:

(1/2)(4-14y)-(y+50)=0


Domain of the equation: 2)(4-14y)!=0

y∈R


We add all the numbers together, and all the variables

(+1/2)(-14y+4)-(y+50)=0

We get rid of parentheses

(+1/2)(-14y+4)-y-50=0

We multiply parentheses ..

(-14y^2+1/2*4)-y-50=0

We multiply all the terms by the denominator


(-14y^2+1-y*2*4)-50*2*4)=0

We add all the numbers together, and all the variables

(-14y^2+1-y*2*4)=0

We get rid of parentheses

-14y^2-y*2*4+1=0

Wy multiply elements

-14y^2-8y*4+1=0

Wy multiply elements

-14y^2-32y+1=0

a = -14; b = -32; c = +1;
Δ = b2-4ac
Δ = -322-4·(-14)·1
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-6\sqrt{30}}{2*-14}=\frac{32-6\sqrt{30}}{-28}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+6\sqrt{30}}{2*-14}=\frac{32+6\sqrt{30}}{-28}
$