(4)(1/16)(1-2x)+5(1/16)=0

Solution for (4)(1/16)(1-2x)+5(1/16)=0 equation:

(4)(1/16)(1-2x)+5(1/16)=0


Domain of the equation: 16)(1-2x)!=0

x∈R


We add all the numbers together, and all the variables

4(+1/16)(-2x+1)+5(+1/16)=0

We multiply parentheses

4(+1/16)(-2x+1)+1/16*5=0

We multiply parentheses ..

4(-2x^2+1/16*1)+1/16*5=0

We calculate fractions


(4(-2x^2+1*16*5)/()+()/()=0


We calculate terms in parentheses: +(4(-2x^2+1*16*5)/()+()/(), so:

4(-2x^2+1*16*5)/()+()/(

We add all the numbers together, and all the variables

4(-2x^2+1*16*5)/()+1

We multiply all the terms by the denominator


4(-2x^2+1*16*5)+1*()

We add all the numbers together, and all the variables

4(-2x^2+1*16*5)

We multiply parentheses

-8x^2+320

Back to the equation:

+(-8x^2+320)


We get rid of parentheses

-8x^2+320=0

a = -8; b = 0; c = +320;
Δ = b2-4ac
Δ = 02-4·(-8)·320
Δ = 10240
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:

$\sqrt{\Delta}=\sqrt{10240}=\sqrt{1024*10}=\sqrt{1024}*\sqrt{10}=32\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{10}}{2*-8}=\frac{0-32\sqrt{10}}{-16}
=-\frac{32\sqrt{10}}{-16}
=-\frac{2\sqrt{10}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{10}}{2*-8}=\frac{0+32\sqrt{10}}{-16}
=\frac{32\sqrt{10}}{-16}
=\frac{2\sqrt{10}}{-1}
$