100=x+2x(2x+5)

Solution for 100=x+2x(2x+5) equation:

100=x+2x(2x+5)

We move all terms to the left:

100-(x+2x(2x+5))=0


We calculate terms in parentheses: -(x+2x(2x+5)), so:

x+2x(2x+5)

We multiply parentheses

4x^2+x+10x

We add all the numbers together, and all the variables

4x^2+11x

Back to the equation:

-(4x^2+11x)


We get rid of parentheses

-4x^2-11x+100=0

a = -4; b = -11; c = +100;
Δ = b2-4ac
Δ = -112-4·(-4)·100
Δ = 1721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{1721}}{2*-4}=\frac{11-\sqrt{1721}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{1721}}{2*-4}=\frac{11+\sqrt{1721}}{-8}
$