-5x(x+1)=x-1+4(3x+2)

Solution for -5x(x+1)=x-1+4(3x+2) equation:

-5x(x+1)=x-1+4(3x+2)

We move all terms to the left:

-5x(x+1)-(x-1+4(3x+2))=0

We multiply parentheses

-5x^2-5x-(x-1+4(3x+2))=0


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

x-1+4(3x+2)

determiningTheFunctionDomain
x+4(3x+2)-1

We multiply parentheses

x+12x+8-1

We add all the numbers together, and all the variables

13x+7

Back to the equation:

-(13x+7)


We get rid of parentheses

-5x^2-5x-13x-7=0

We add all the numbers together, and all the variables

-5x^2-18x-7=0

a = -5; b = -18; c = -7;
Δ = b2-4ac
Δ = -182-4·(-5)·(-7)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{46}}{2*-5}=\frac{18-2\sqrt{46}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{46}}{2*-5}=\frac{18+2\sqrt{46}}{-10}
$