6(x+4)+2(x+1)=(x+1)(x+4)

Solution for 6(x+4)+2(x+1)=(x+1)(x+4) equation:

6(x+4)+2(x+1)=(x+1)(x+4)

We move all terms to the left:

6(x+4)+2(x+1)-((x+1)(x+4))=0

We multiply parentheses

6x+2x-((x+1)(x+4))+24+2=0

We multiply parentheses ..

-((+x^2+4x+x+4))+6x+2x+24+2=0


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

(+x^2+4x+x+4)

We get rid of parentheses

x^2+4x+x+4

We add all the numbers together, and all the variables

x^2+5x+4

Back to the equation:

-(x^2+5x+4)


We add all the numbers together, and all the variables

8x-(x^2+5x+4)+26=0

We get rid of parentheses

-x^2+8x-5x-4+26=0

We add all the numbers together, and all the variables

-1x^2+3x+22=0

a = -1; b = 3; c = +22;
Δ = b2-4ac
Δ = 32-4·(-1)·22
Δ = 97
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{-(3)-\sqrt{97}}{2*-1}=\frac{-3-\sqrt{97}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{97}}{2*-1}=\frac{-3+\sqrt{97}}{-2}
$