3x-10+2x+1+8/9x+10=180

Solution for 3x-10+2x+1+8/9x+10=180 equation:

3x-10+2x+1+8/9x+10=180

We move all terms to the left:

3x-10+2x+1+8/9x+10-(180)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

5x+8/9x-179=0

We multiply all the terms by the denominator


5x*9x-179*9x+8=0

Wy multiply elements

45x^2-1611x+8=0

a = 45; b = -1611; c = +8;
Δ = b2-4ac
Δ = -16112-4·45·8
Δ = 2593881
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:

$\sqrt{\Delta}=\sqrt{2593881}=\sqrt{9*288209}=\sqrt{9}*\sqrt{288209}=3\sqrt{288209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1611)-3\sqrt{288209}}{2*45}=\frac{1611-3\sqrt{288209}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1611)+3\sqrt{288209}}{2*45}=\frac{1611+3\sqrt{288209}}{90}
$