(2x-30)+(2/3x+15)=180

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Solution for (2x-30)+(2/3x+15)=180 equation:



(2x-30)+(2/3x+15)=180
We move all terms to the left:
(2x-30)+(2/3x+15)-(180)=0
Domain of the equation: 3x+15)!=0
x∈R
We get rid of parentheses
2x+2/3x-30+15-180=0
We multiply all the terms by the denominator
2x*3x-30*3x+15*3x-180*3x+2=0
Wy multiply elements
6x^2-90x+45x-540x+2=0
We add all the numbers together, and all the variables
6x^2-585x+2=0
a = 6; b = -585; c = +2;
Δ = b2-4ac
Δ = -5852-4·6·2
Δ = 342177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-585)-\sqrt{342177}}{2*6}=\frac{585-\sqrt{342177}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-585)+\sqrt{342177}}{2*6}=\frac{585+\sqrt{342177}}{12} $

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