4(2x+1)=-2x(x+13)

Solution for 4(2x+1)=-2x(x+13) equation:

4(2x+1)=-2x(x+13)

We move all terms to the left:

4(2x+1)-(-2x(x+13))=0

We multiply parentheses

8x-(-2x(x+13))+4=0


We calculate terms in parentheses: -(-2x(x+13)), so:

-2x(x+13)

We multiply parentheses

-2x^2-26x

Back to the equation:

-(-2x^2-26x)


We get rid of parentheses

2x^2+26x+8x+4=0

We add all the numbers together, and all the variables

2x^2+34x+4=0

a = 2; b = 34; c = +4;
Δ = b2-4ac
Δ = 342-4·2·4
Δ = 1124
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:

$\sqrt{\Delta}=\sqrt{1124}=\sqrt{4*281}=\sqrt{4}*\sqrt{281}=2\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{281}}{2*2}=\frac{-34-2\sqrt{281}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{281}}{2*2}=\frac{-34+2\sqrt{281}}{4}
$