x(x-4)=-3.5

Solution for x(x-4)=-3.5 equation:

x(x-4)=-3.5

We move all terms to the left:

x(x-4)-(-3.5)=0

We add all the numbers together, and all the variables

x(x-4)+3.5=0

We multiply parentheses

x^2-4x+3.5=0

a = 1; b = -4; c = +3.5;
Δ = b2-4ac
Δ = -42-4·1·3.5
Δ = 2
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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