1/4x+-32=7+4x

Solution for 1/4x+-32=7+4x equation:

1/4x+-32=7+4x

We move all terms to the left:

1/4x+-32-(7+4x)=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-(4x+7)-32+=0

We add all the numbers together, and all the variables

1/4x-(4x+7)=0

We get rid of parentheses

1/4x-4x-7=0

We multiply all the terms by the denominator


-4x*4x-7*4x+1=0

Wy multiply elements

-16x^2-28x+1=0

a = -16; b = -28; c = +1;
Δ = b2-4ac
Δ = -282-4·(-16)·1
Δ = 848
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:

$\sqrt{\Delta}=\sqrt{848}=\sqrt{16*53}=\sqrt{16}*\sqrt{53}=4\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{53}}{2*-16}=\frac{28-4\sqrt{53}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{53}}{2*-16}=\frac{28+4\sqrt{53}}{-32}
$