40(x+4)+3(x+1)(x+4)=40(x+1)(x+3)

Solution for 40(x+4)+3(x+1)(x+4)=40(x+1)(x+3) equation:

40(x+4)+3(x+1)(x+4)=40(x+1)(x+3)

We move all terms to the left:

40(x+4)+3(x+1)(x+4)-(40(x+1)(x+3))=0

We multiply parentheses

40x+3(x+1)(x+4)-(40(x+1)(x+3))+160=0

We multiply parentheses ..

3(+x^2+4x+x+4)+40x-(40(x+1)(x+3))+160=0


We calculate terms in parentheses: -(40(x+1)(x+3)), so:

40(x+1)(x+3)

We multiply parentheses ..

40(+x^2+3x+x+3)

We multiply parentheses

40x^2+120x+40x+120

We add all the numbers together, and all the variables

40x^2+160x+120

Back to the equation:

-(40x^2+160x+120)


We multiply parentheses

3x^2+12x+3x+40x-(40x^2+160x+120)+12+160=0

We get rid of parentheses

3x^2-40x^2+12x+3x+40x-160x-120+12+160=0

We add all the numbers together, and all the variables

-37x^2-105x+52=0

a = -37; b = -105; c = +52;
Δ = b2-4ac
Δ = -1052-4·(-37)·52
Δ = 18721
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{-(-105)-\sqrt{18721}}{2*-37}=\frac{105-\sqrt{18721}}{-74}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{18721}}{2*-37}=\frac{105+\sqrt{18721}}{-74}
$