4x(x-26)=-200

Solution for 4x(x-26)=-200 equation:

4x(x-26)=-200

We move all terms to the left:

4x(x-26)-(-200)=0

We add all the numbers together, and all the variables

4x(x-26)+200=0

We multiply parentheses

4x^2-104x+200=0

a = 4; b = -104; c = +200;
Δ = b2-4ac
Δ = -1042-4·4·200
Δ = 7616
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:

$\sqrt{\Delta}=\sqrt{7616}=\sqrt{64*119}=\sqrt{64}*\sqrt{119}=8\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-8\sqrt{119}}{2*4}=\frac{104-8\sqrt{119}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+8\sqrt{119}}{2*4}=\frac{104+8\sqrt{119}}{8}
$