(X+3)(x+7)=(x+1)(3x+1)

Solution for (X+3)(x+7)=(x+1)(3x+1) equation:

(X+3)(X+7)=(X+1)(3X+1)

We move all terms to the left:

(X+3)(X+7)-((X+1)(3X+1))=0

We multiply parentheses ..

(+X^2+7X+3X+21)-((X+1)(3X+1))=0


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

(X+1)(3X+1)

We multiply parentheses ..

(+3X^2+X+3X+1)

We get rid of parentheses

3X^2+X+3X+1

We add all the numbers together, and all the variables

3X^2+4X+1

Back to the equation:

-(3X^2+4X+1)


We get rid of parentheses

X^2-3X^2+7X+3X-4X+21-1=0

We add all the numbers together, and all the variables

-2X^2+6X+20=0

a = -2; b = 6; c = +20;
Δ = b2-4ac
Δ = 62-4·(-2)·20
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*-2}=\frac{-20}{-4}
=+5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*-2}=\frac{8}{-4}
=-2
$