-0.5(x-1)(x-7)=0

Solution for -0.5(x-1)(x-7)=0 equation:

-0.5(x-1)(x-7)=0

We multiply parentheses ..

-0.5(+x^2-7x-1x+7)=0

We multiply parentheses

-0.5x^2+3.5x+0.5x-3.5=0

We add all the numbers together, and all the variables

-0.5x^2+4x-3.5=0

a = -0.5; b = 4; c = -3.5;
Δ = b2-4ac
Δ = 42-4·(-0.5)·(-3.5)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-3}{2*-0.5}=\frac{-7}{-1}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+3}{2*-0.5}=\frac{-1}{-1}
=1
$