(6+2x)(4+2x)=55.25

Solution for (6+2x)(4+2x)=55.25 equation:

(6+2x)(4+2x)=55.25

We move all terms to the left:

(6+2x)(4+2x)-(55.25)=0

We add all the numbers together, and all the variables

(2x+6)(2x+4)-(55.25)=0

We add all the numbers together, and all the variables

(2x+6)(2x+4)-55.25=0

We multiply parentheses ..

(+4x^2+8x+12x+24)-55.25=0

We get rid of parentheses

4x^2+8x+12x+24-55.25=0

We add all the numbers together, and all the variables

4x^2+20x-31.25=0

a = 4; b = 20; c = -31.25;
Δ = b2-4ac
Δ = 202-4·4·(-31.25)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-30}{2*4}=\frac{-50}{8}
=-6+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+30}{2*4}=\frac{10}{8}
=1+1/4
$