(X+1)(6x)=(x+1)(30)

Solution for (X+1)(6x)=(x+1)(30) equation:

(X+1)(6X)=(X+1)(30)

We move all terms to the left:

(X+1)(6X)-((X+1)(30))=0

We multiply parentheses

6X^2+6X-((X+1)30)=0


We calculate terms in parentheses: -((X+1)30), so:

(X+1)30

We multiply parentheses

30X+30

Back to the equation:

-(30X+30)


We get rid of parentheses

6X^2+6X-30X-30=0

We add all the numbers together, and all the variables

6X^2-24X-30=0

a = 6; b = -24; c = -30;
Δ = b2-4ac
Δ = -242-4·6·(-30)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-36}{2*6}=\frac{-12}{12}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+36}{2*6}=\frac{60}{12}
=5
$