1/4x+32=-x+11

Solution for 1/4x+32=-x+11 equation:

1/4x+32=-x+11

We move all terms to the left:

1/4x+32-(-x+11)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(-1x+11)+32=0

We get rid of parentheses

1/4x+1x-11+32=0

We multiply all the terms by the denominator


1x*4x-11*4x+32*4x+1=0

Wy multiply elements

4x^2-44x+128x+1=0

We add all the numbers together, and all the variables

4x^2+84x+1=0

a = 4; b = 84; c = +1;
Δ = b2-4ac
Δ = 842-4·4·1
Δ = 7040
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7040}=\sqrt{64*110}=\sqrt{64}*\sqrt{110}=8\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-8\sqrt{110}}{2*4}=\frac{-84-8\sqrt{110}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+8\sqrt{110}}{2*4}=\frac{-84+8\sqrt{110}}{8}
$