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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

-2x(x-26)

We multiply parentheses

-2x^2+52x

Back to the equation:

-(-2x^2+52x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-48x+4=0

a = 2; b = -48; c = +4;
Δ = b2-4ac
Δ = -482-4·2·4
Δ = 2272
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:

$\sqrt{\Delta}=\sqrt{2272}=\sqrt{16*142}=\sqrt{16}*\sqrt{142}=4\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{142}}{2*2}=\frac{48-4\sqrt{142}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{142}}{2*2}=\frac{48+4\sqrt{142}}{4}
$