216=4x(25+x)

Solution for 216=4x(25+x) equation:

216=4x(25+x)

We move all terms to the left:

216-(4x(25+x))=0

We add all the numbers together, and all the variables

-(4x(x+25))+216=0


We calculate terms in parentheses: -(4x(x+25)), so:

4x(x+25)

We multiply parentheses

4x^2+100x

Back to the equation:

-(4x^2+100x)


We get rid of parentheses

-4x^2-100x+216=0

a = -4; b = -100; c = +216;
Δ = b2-4ac
Δ = -1002-4·(-4)·216
Δ = 13456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13456}=116$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-116}{2*-4}=\frac{-16}{-8}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+116}{2*-4}=\frac{216}{-8}
=-27
$