3/4x-24+2x=180

Solution for 3/4x-24+2x=180 equation:

3/4x-24+2x=180

We move all terms to the left:

3/4x-24+2x-(180)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x+3/4x-204=0

We multiply all the terms by the denominator


2x*4x-204*4x+3=0

Wy multiply elements

8x^2-816x+3=0

a = 8; b = -816; c = +3;
Δ = b2-4ac
Δ = -8162-4·8·3
Δ = 665760
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:

$\sqrt{\Delta}=\sqrt{665760}=\sqrt{16*41610}=\sqrt{16}*\sqrt{41610}=4\sqrt{41610}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-816)-4\sqrt{41610}}{2*8}=\frac{816-4\sqrt{41610}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-816)+4\sqrt{41610}}{2*8}=\frac{816+4\sqrt{41610}}{16}
$