0.5(1/3x+1)(2x-10)=0

Solution for 0.5(1/3x+1)(2x-10)=0 equation:

0.5(1/3x+1)(2x-10)=0


Domain of the equation: 3x+1)(2x-10)!=0

x∈R


We multiply parentheses ..

0.5(+2x^2-10x+2x-10)=0

We multiply parentheses

x^2-5x+x-5=0

We add all the numbers together, and all the variables

x^2-4x-5=0

a = 1; b = -4; c = -5;
Δ = b2-4ac
Δ = -42-4·1·(-5)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6}{2*1}=\frac{10}{2}
=5
$