4x(x+1)=(2x+5)

Solution for 4x(x+1)=(2x+5) equation:

4x(x+1)=(2x+5)

We move all terms to the left:

4x(x+1)-((2x+5))=0

We multiply parentheses

4x^2+4x-((2x+5))=0


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

(2x+5)

We get rid of parentheses

2x+5

Back to the equation:

-(2x+5)


We get rid of parentheses

4x^2+4x-2x-5=0

We add all the numbers together, and all the variables

4x^2+2x-5=0

a = 4; b = 2; c = -5;
Δ = b2-4ac
Δ = 22-4·4·(-5)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{21}}{2*4}=\frac{-2-2\sqrt{21}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{21}}{2*4}=\frac{-2+2\sqrt{21}}{8}
$