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

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

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

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-2x*4x-6*4x-3*4x-90*4x+1=0

Wy multiply elements

-8x^2-24x-12x-360x+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 = 156848
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:

$\sqrt{\Delta}=\sqrt{156848}=\sqrt{16*9803}=\sqrt{16}*\sqrt{9803}=4\sqrt{9803}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-396)-4\sqrt{9803}}{2*-8}=\frac{396-4\sqrt{9803}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-396)+4\sqrt{9803}}{2*-8}=\frac{396+4\sqrt{9803}}{-16}
$