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

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

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

We move all terms to the left:

2x-1+3x+10-3+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-164=0

We multiply all the terms by the denominator


5x*9x-164*9x+8=0

Wy multiply elements

45x^2-1476x+8=0

a = 45; b = -1476; c = +8;
Δ = b2-4ac
Δ = -14762-4·45·8
Δ = 2177136
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:

$\sqrt{\Delta}=\sqrt{2177136}=\sqrt{144*15119}=\sqrt{144}*\sqrt{15119}=12\sqrt{15119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1476)-12\sqrt{15119}}{2*45}=\frac{1476-12\sqrt{15119}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1476)+12\sqrt{15119}}{2*45}=\frac{1476+12\sqrt{15119}}{90}
$