(7x+1)(7x+5)=(3x+1)(5x+1)

Solution for (7x+1)(7x+5)=(3x+1)(5x+1) equation:

(7x+1)(7x+5)=(3x+1)(5x+1)

We move all terms to the left:

(7x+1)(7x+5)-((3x+1)(5x+1))=0

We multiply parentheses ..

(+49x^2+35x+7x+5)-((3x+1)(5x+1))=0


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

(3x+1)(5x+1)

We multiply parentheses ..

(+15x^2+3x+5x+1)

We get rid of parentheses

15x^2+3x+5x+1

We add all the numbers together, and all the variables

15x^2+8x+1

Back to the equation:

-(15x^2+8x+1)


We get rid of parentheses

49x^2-15x^2+35x+7x-8x+5-1=0

We add all the numbers together, and all the variables

34x^2+34x+4=0

a = 34; b = 34; c = +4;
Δ = b2-4ac
Δ = 342-4·34·4
Δ = 612
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-6\sqrt{17}}{2*34}=\frac{-34-6\sqrt{17}}{68}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+6\sqrt{17}}{2*34}=\frac{-34+6\sqrt{17}}{68}
$