180=-2x-6-1/4x-3+90

Solution for 180=-2x-6-1/4x-3+90 equation:

180=-2x-6-1/4x-3+90

We move all terms to the left:

180-(-2x-6-1/4x-3+90)=0


Domain of the equation: 4x-3+90)!=0

We move all terms containing x to the left, all other terms to the right

4x+90)!=3

x∈R


We add all the numbers together, and all the variables

-(-2x-1/4x+81)+180=0

We get rid of parentheses

2x+1/4x-81+180=0

We multiply all the terms by the denominator


2x*4x-81*4x+180*4x+1=0

Wy multiply elements

8x^2-324x+720x+1=0

We add all the numbers together, and all the variables

8x^2+396x+1=0

a = 8; b = 396; c = +1;
Δ = b2-4ac
Δ = 3962-4·8·1
Δ = 156784
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:

$\sqrt{\Delta}=\sqrt{156784}=\sqrt{16*9799}=\sqrt{16}*\sqrt{9799}=4\sqrt{9799}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(396)-4\sqrt{9799}}{2*8}=\frac{-396-4\sqrt{9799}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(396)+4\sqrt{9799}}{2*8}=\frac{-396+4\sqrt{9799}}{16}
$