(12x+8x)/4=5x*

Solution for (12x+8x)/4=5x* equation:

(12x+8x)/4=5x*

We move all terms to the left:

(12x+8x)/4-(5x*)=0

We add all the numbers together, and all the variables

(+20x)/4-(+5x*)=0

We get rid of parentheses

(+20x)/4-5x*=0

We multiply all the terms by the denominator


(+20x)-(5x*)*4=0

We add all the numbers together, and all the variables

(+20x)-(+5x*)*4=0

We multiply parentheses

-20x^2+(+20x)=0

We get rid of parentheses

-20x^2+20x=0

a = -20; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-20)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-20}=\frac{-40}{-40}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-20}=\frac{0}{-40}
=0
$