(9+2x)(5+2x)=77

Solution for (9+2x)(5+2x)=77 equation:

(9+2x)(5+2x)=77

We move all terms to the left:

(9+2x)(5+2x)-(77)=0

We add all the numbers together, and all the variables

(2x+9)(2x+5)-77=0

We multiply parentheses ..

(+4x^2+10x+18x+45)-77=0

We get rid of parentheses

4x^2+10x+18x+45-77=0

We add all the numbers together, and all the variables

4x^2+28x-32=0

a = 4; b = 28; c = -32;
Δ = b2-4ac
Δ = 282-4·4·(-32)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-36}{2*4}=\frac{-64}{8}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+36}{2*4}=\frac{8}{8}
=1
$