4x(x+1)=-2(x-26)

Solution for 4x(x+1)=-2(x-26) equation:

4x(x+1)=-2(x-26)

We move all terms to the left:

4x(x+1)-(-2(x-26))=0

We multiply parentheses

4x^2+4x-(-2(x-26))=0


We calculate terms in parentheses: -(-2(x-26)), so:

-2(x-26)

We multiply parentheses

-2x+52

Back to the equation:

-(-2x+52)


We get rid of parentheses

4x^2+4x+2x-52=0

We add all the numbers together, and all the variables

4x^2+6x-52=0

a = 4; b = 6; c = -52;
Δ = b2-4ac
Δ = 62-4·4·(-52)
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{217}}{2*4}=\frac{-6-2\sqrt{217}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{217}}{2*4}=\frac{-6+2\sqrt{217}}{8}
$