0.1(x-1)(3x-14)=0

Solution for 0.1(x-1)(3x-14)=0 equation:

0.1(x-1)(3x-14)=0

We multiply parentheses ..

0.1(+3x^2-14x-3x+14)=0

We multiply parentheses

0.3x^2-1.4x-0.3x+1.4=0

We add all the numbers together, and all the variables

0.3x^2-1.7x+1.4=0

a = 0.3; b = -1.7; c = +1.4;
Δ = b2-4ac
Δ = -1.72-4·0.3·1.4
Δ = 1.21
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{-(-1.7)-\sqrt{1.21}}{2*0.3}=\frac{1.7-\sqrt{1.21}}{0.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.7)+\sqrt{1.21}}{2*0.3}=\frac{1.7+\sqrt{1.21}}{0.6}
$