3/4x-13+3x-17=180

Solution for 3/4x-13+3x-17=180 equation:

3/4x-13+3x-17=180

We move all terms to the left:

3/4x-13+3x-17-(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

3x+3/4x-210=0

We multiply all the terms by the denominator


3x*4x-210*4x+3=0

Wy multiply elements

12x^2-840x+3=0

a = 12; b = -840; c = +3;
Δ = b2-4ac
Δ = -8402-4·12·3
Δ = 705456
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:

$\sqrt{\Delta}=\sqrt{705456}=\sqrt{144*4899}=\sqrt{144}*\sqrt{4899}=12\sqrt{4899}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-840)-12\sqrt{4899}}{2*12}=\frac{840-12\sqrt{4899}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-840)+12\sqrt{4899}}{2*12}=\frac{840+12\sqrt{4899}}{24}
$