(3+2x)(7+2x)=50

Solution for (3+2x)(7+2x)=50 equation:

(3+2x)(7+2x)=50

We move all terms to the left:

(3+2x)(7+2x)-(50)=0

We add all the numbers together, and all the variables

(2x+3)(2x+7)-50=0

We multiply parentheses ..

(+4x^2+14x+6x+21)-50=0

We get rid of parentheses

4x^2+14x+6x+21-50=0

We add all the numbers together, and all the variables

4x^2+20x-29=0

a = 4; b = 20; c = -29;
Δ = b2-4ac
Δ = 202-4·4·(-29)
Δ = 864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-12\sqrt{6}}{2*4}=\frac{-20-12\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+12\sqrt{6}}{2*4}=\frac{-20+12\sqrt{6}}{8}
$