4(x-1)x=3(x+5)-114x-4-x=3x+15-113x-4=3x+4

Solution for 4(x-1)x=3(x+5)-114x-4-x=3x+15-113x-4=3x+4 equation:

4(x-1)x=3(x+5)-114x-4-x=3x+15-113x-4=3x+4

We move all terms to the left:

4(x-1)x-(3(x+5)-114x-4-x)=0

We multiply parentheses

4x^2-4x-(3(x+5)-114x-4-x)=0


We calculate terms in parentheses: -(3(x+5)-114x-4-x), so:

3(x+5)-114x-4-x

determiningTheFunctionDomain
3(x+5)-114x-x-4

We add all the numbers together, and all the variables

-115x+3(x+5)-4

We multiply parentheses

-115x+3x+15-4

We add all the numbers together, and all the variables

-112x+11

Back to the equation:

-(-112x+11)


We get rid of parentheses

4x^2-4x+112x-11=0

We add all the numbers together, and all the variables

4x^2+108x-11=0

a = 4; b = 108; c = -11;
Δ = b2-4ac
Δ = 1082-4·4·(-11)
Δ = 11840
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:

$\sqrt{\Delta}=\sqrt{11840}=\sqrt{64*185}=\sqrt{64}*\sqrt{185}=8\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-8\sqrt{185}}{2*4}=\frac{-108-8\sqrt{185}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+8\sqrt{185}}{2*4}=\frac{-108+8\sqrt{185}}{8}
$