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

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

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

We move all terms to the left:

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


Domain of the equation: 9x+10)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


2x*9x+3x*9x+1*9x+10*9x+10*9x-180*9x+8=0

Wy multiply elements

18x^2+27x^2+9x+90x+90x-1620x+8=0

We add all the numbers together, and all the variables

45x^2-1431x+8=0

a = 45; b = -1431; c = +8;
Δ = b2-4ac
Δ = -14312-4·45·8
Δ = 2046321
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:

$\sqrt{\Delta}=\sqrt{2046321}=\sqrt{9*227369}=\sqrt{9}*\sqrt{227369}=3\sqrt{227369}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1431)-3\sqrt{227369}}{2*45}=\frac{1431-3\sqrt{227369}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1431)+3\sqrt{227369}}{2*45}=\frac{1431+3\sqrt{227369}}{90}
$