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

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

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

We move all terms to the left:

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

We multiply parentheses

4X^2-8X-(-3+5X(X+1))+1=0


We calculate terms in parentheses: -(-3+5X(X+1)), so:

-3+5X(X+1)

determiningTheFunctionDomain
5X(X+1)-3

We multiply parentheses

5X^2+5X-3

Back to the equation:

-(5X^2+5X-3)


We get rid of parentheses

4X^2-5X^2-8X-5X+3+1=0

We add all the numbers together, and all the variables

-1X^2-13X+4=0

a = -1; b = -13; c = +4;
Δ = b2-4ac
Δ = -132-4·(-1)·4
Δ = 185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{185}}{2*-1}=\frac{13-\sqrt{185}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{185}}{2*-1}=\frac{13+\sqrt{185}}{-2}
$