3x-16=(1/4)(4x-16)

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

3x-16=(1/4)(4x-16)

We move all terms to the left:

3x-16-((1/4)(4x-16))=0


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

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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


We calculate terms in parentheses: -((+4x^2+1+3x*4*-16)), so:

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

We get rid of parentheses

4x^2+3x*4*+1-16

We add all the numbers together, and all the variables

4x^2+3x*4*-15

Wy multiply elements

4x^2+12x^2-15

We add all the numbers together, and all the variables

16x^2-15

Back to the equation:

-(16x^2-15)


We add all the numbers together, and all the variables

-(16x^2-15)=0

We get rid of parentheses

-16x^2+15=0

a = -16; b = 0; c = +15;
Δ = b2-4ac
Δ = 02-4·(-16)·15
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*-16}=\frac{0-8\sqrt{15}}{-32}
=-\frac{8\sqrt{15}}{-32}
=-\frac{\sqrt{15}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*-16}=\frac{0+8\sqrt{15}}{-32}
=\frac{8\sqrt{15}}{-32}
=\frac{\sqrt{15}}{-4}
$