(25+2w)(14+2w)=432

Solution for (25+2w)(14+2w)=432 equation:

(25+2w)(14+2w)=432

We move all terms to the left:

(25+2w)(14+2w)-(432)=0

We add all the numbers together, and all the variables

(2w+25)(2w+14)-432=0

We multiply parentheses ..

(+4w^2+28w+50w+350)-432=0

We get rid of parentheses

4w^2+28w+50w+350-432=0

We add all the numbers together, and all the variables

4w^2+78w-82=0

a = 4; b = 78; c = -82;
Δ = b2-4ac
Δ = 782-4·4·(-82)
Δ = 7396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7396}=86$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-86}{2*4}=\frac{-164}{8}
=-20+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+86}{2*4}=\frac{8}{8}
=1
$