(5x+1)(5x+1)=(x+11)(x+2)

Solution for (5x+1)(5x+1)=(x+11)(x+2) equation:

(5x+1)(5x+1)=(x+11)(x+2)

We move all terms to the left:

(5x+1)(5x+1)-((x+11)(x+2))=0

We multiply parentheses ..

(+25x^2+5x+5x+1)-((x+11)(x+2))=0


We calculate terms in parentheses: -((x+11)(x+2)), so:

(x+11)(x+2)

We multiply parentheses ..

(+x^2+2x+11x+22)

We get rid of parentheses

x^2+2x+11x+22

We add all the numbers together, and all the variables

x^2+13x+22

Back to the equation:

-(x^2+13x+22)


We get rid of parentheses

25x^2-x^2+5x+5x-13x+1-22=0

We add all the numbers together, and all the variables

24x^2-3x-21=0

a = 24; b = -3; c = -21;
Δ = b2-4ac
Δ = -32-4·24·(-21)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-45}{2*24}=\frac{-42}{48}
=-7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+45}{2*24}=\frac{48}{48}
=1
$