(12+2x)(7+2x)-84=92

Solution for (12+2x)(7+2x)-84=92 equation:

(12+2x)(7+2x)-84=92

We move all terms to the left:

(12+2x)(7+2x)-84-(92)=0

We add all the numbers together, and all the variables

(2x+12)(2x+7)-84-92=0

We add all the numbers together, and all the variables

(2x+12)(2x+7)-176=0

We multiply parentheses ..

(+4x^2+14x+24x+84)-176=0

We get rid of parentheses

4x^2+14x+24x+84-176=0

We add all the numbers together, and all the variables

4x^2+38x-92=0

a = 4; b = 38; c = -92;
Δ = b2-4ac
Δ = 382-4·4·(-92)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-54}{2*4}=\frac{-92}{8}
=-11+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+54}{2*4}=\frac{16}{8}
=2
$