0.05(x-1.5)(x-8)=400

Solution for 0.05(x-1.5)(x-8)=400 equation:

0.05(x-1.5)(x-8)=400

We move all terms to the left:

0.05(x-1.5)(x-8)-(400)=0

We multiply parentheses ..

0.05(+x^2-8x-1.5x+12)-400=0

We multiply parentheses

0.05x^2-0.4x-0.05x+0.6-400=0

We add all the numbers together, and all the variables

0.05x^2-0.45x-399.4=0

a = 0.05; b = -0.45; c = -399.4;
Δ = b2-4ac
Δ = -0.452-4·0.05·(-399.4)
Δ = 80.0825
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{-(-0.45)-\sqrt{80.0825}}{2*0.05}=\frac{0.45-\sqrt{80.0825}}{0.1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.45)+\sqrt{80.0825}}{2*0.05}=\frac{0.45+\sqrt{80.0825}}{0.1}
$