2/3x+25+3(5/12x-25)=180

Solution for 2/3x+25+3(5/12x-25)=180 equation:

2/3x+25+3(5/12x-25)=180

We move all terms to the left:

2/3x+25+3(5/12x-25)-(180)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 12x-25)!=0

x∈R


We add all the numbers together, and all the variables

2/3x+3(5/12x-25)-155=0

We multiply parentheses

2/3x+15x-75-155=0

We multiply all the terms by the denominator


15x*3x-75*3x-155*3x+2=0

Wy multiply elements

45x^2-225x-465x+2=0

We add all the numbers together, and all the variables

45x^2-690x+2=0

a = 45; b = -690; c = +2;
Δ = b2-4ac
Δ = -6902-4·45·2
Δ = 475740
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:

$\sqrt{\Delta}=\sqrt{475740}=\sqrt{36*13215}=\sqrt{36}*\sqrt{13215}=6\sqrt{13215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-690)-6\sqrt{13215}}{2*45}=\frac{690-6\sqrt{13215}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-690)+6\sqrt{13215}}{2*45}=\frac{690+6\sqrt{13215}}{90}
$