16x(x+1)=4(13+3x)

Solution for 16x(x+1)=4(13+3x) equation:

16x(x+1)=4(13+3x)

We move all terms to the left:

16x(x+1)-(4(13+3x))=0

We add all the numbers together, and all the variables

16x(x+1)-(4(3x+13))=0

We multiply parentheses

16x^2+16x-(4(3x+13))=0


We calculate terms in parentheses: -(4(3x+13)), so:

4(3x+13)

We multiply parentheses

12x+52

Back to the equation:

-(12x+52)


We get rid of parentheses

16x^2+16x-12x-52=0

We add all the numbers together, and all the variables

16x^2+4x-52=0

a = 16; b = 4; c = -52;
Δ = b2-4ac
Δ = 42-4·16·(-52)
Δ = 3344
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:

$\sqrt{\Delta}=\sqrt{3344}=\sqrt{16*209}=\sqrt{16}*\sqrt{209}=4\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{209}}{2*16}=\frac{-4-4\sqrt{209}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{209}}{2*16}=\frac{-4+4\sqrt{209}}{32}
$