X+5=4x(x+2)

Solution for X+5=4x(x+2) equation:

X+5=4X(X+2)

We move all terms to the left:

X+5-(4X(X+2))=0


We calculate terms in parentheses: -(4X(X+2)), so:

4X(X+2)

We multiply parentheses

4X^2+8X

Back to the equation:

-(4X^2+8X)


We get rid of parentheses

-4X^2+X-8X+5=0

We add all the numbers together, and all the variables

-4X^2-7X+5=0

a = -4; b = -7; c = +5;
Δ = b2-4ac
Δ = -72-4·(-4)·5
Δ = 129
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{-(-7)-\sqrt{129}}{2*-4}=\frac{7-\sqrt{129}}{-8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{129}}{2*-4}=\frac{7+\sqrt{129}}{-8}
$