4(x+5)=(x+2)(x+2)

Solution for 4(x+5)=(x+2)(x+2) equation:

4(x+5)=(x+2)(x+2)

We move all terms to the left:

4(x+5)-((x+2)(x+2))=0

We multiply parentheses

4x-((x+2)(x+2))+20=0

We multiply parentheses ..

-((+x^2+2x+2x+4))+4x+20=0


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

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

We get rid of parentheses

x^2+2x+2x+4

We add all the numbers together, and all the variables

x^2+4x+4

Back to the equation:

-(x^2+4x+4)


We add all the numbers together, and all the variables

4x-(x^2+4x+4)+20=0

We get rid of parentheses

-x^2+4x-4x-4+20=0

We add all the numbers together, and all the variables

-1x^2+16=0

a = -1; b = 0; c = +16;
Δ = b2-4ac
Δ = 02-4·(-1)·16
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*-1}=\frac{8}{-2}
=-4
$