(1/4)(8x+16)-3x=33

Solution for (1/4)(8x+16)-3x=33 equation:

(1/4)(8x+16)-3x=33

We move all terms to the left:

(1/4)(8x+16)-3x-(33)=0


Domain of the equation: 4)(8x+16)!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)(8x+16)-3x-33=0

We add all the numbers together, and all the variables

-3x+(+1/4)(8x+16)-33=0

We multiply parentheses ..

(+8x^2+1/4*16)-3x-33=0

We multiply all the terms by the denominator


(+8x^2+1-3x*4*16)-33*4*16)=0

We add all the numbers together, and all the variables

(+8x^2+1-3x*4*16)=0

We get rid of parentheses

8x^2-3x*4*16+1=0

Wy multiply elements

8x^2-192x*1+1=0

Wy multiply elements

8x^2-192x+1=0

a = 8; b = -192; c = +1;
Δ = b2-4ac
Δ = -1922-4·8·1
Δ = 36832
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:

$\sqrt{\Delta}=\sqrt{36832}=\sqrt{16*2302}=\sqrt{16}*\sqrt{2302}=4\sqrt{2302}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-4\sqrt{2302}}{2*8}=\frac{192-4\sqrt{2302}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+4\sqrt{2302}}{2*8}=\frac{192+4\sqrt{2302}}{16}
$