(4x-8)+(1/4)x=180

Solution for (4x-8)+(1/4)x=180 equation:

(4x-8)+(1/4)x=180

We move all terms to the left:

(4x-8)+(1/4)x-(180)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(4x-8)+(+1/4)x-180=0

We multiply parentheses

x^2+(4x-8)-180=0

We get rid of parentheses

x^2+4x-8-180=0

We add all the numbers together, and all the variables

x^2+4x-188=0

a = 1; b = 4; c = -188;
Δ = b2-4ac
Δ = 42-4·1·(-188)
Δ = 768
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-16\sqrt{3}}{2*1}=\frac{-4-16\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+16\sqrt{3}}{2*1}=\frac{-4+16\sqrt{3}}{2}
$