(5+2x)(10+2x)=84

Solution for (5+2x)(10+2x)=84 equation:

(5+2x)(10+2x)=84

We move all terms to the left:

(5+2x)(10+2x)-(84)=0

We add all the numbers together, and all the variables

(2x+5)(2x+10)-84=0

We multiply parentheses ..

(+4x^2+20x+10x+50)-84=0

We get rid of parentheses

4x^2+20x+10x+50-84=0

We add all the numbers together, and all the variables

4x^2+30x-34=0

a = 4; b = 30; c = -34;
Δ = b2-4ac
Δ = 302-4·4·(-34)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-38}{2*4}=\frac{-68}{8}
=-8+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+38}{2*4}=\frac{8}{8}
=1
$