4x(x-1)=14-(4x-1)

Solution for 4x(x-1)=14-(4x-1) equation:

4x(x-1)=14-(4x-1)

We move all terms to the left:

4x(x-1)-(14-(4x-1))=0

We multiply parentheses

4x^2-4x-(14-(4x-1))=0


We calculate terms in parentheses: -(14-(4x-1)), so:

14-(4x-1)

determiningTheFunctionDomain
-(4x-1)+14

We get rid of parentheses

-4x+1+14

We add all the numbers together, and all the variables

-4x+15

Back to the equation:

-(-4x+15)


We get rid of parentheses

4x^2-4x+4x-15=0

We add all the numbers together, and all the variables

4x^2-15=0

a = 4; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·4·(-15)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*4}=\frac{0-4\sqrt{15}}{8}
=-\frac{4\sqrt{15}}{8}
=-\frac{\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*4}=\frac{0+4\sqrt{15}}{8}
=\frac{4\sqrt{15}}{8}
=\frac{\sqrt{15}}{2}
$