85+2x=-2/3x+45

Solution for 85+2x=-2/3x+45 equation:

85+2x=-2/3x+45

We move all terms to the left:

85+2x-(-2/3x+45)=0


Domain of the equation: 3x+45)!=0

x∈R


We get rid of parentheses

2x+2/3x-45+85=0

We multiply all the terms by the denominator


2x*3x-45*3x+85*3x+2=0

Wy multiply elements

6x^2-135x+255x+2=0

We add all the numbers together, and all the variables

6x^2+120x+2=0

a = 6; b = 120; c = +2;
Δ = b2-4ac
Δ = 1202-4·6·2
Δ = 14352
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:

$\sqrt{\Delta}=\sqrt{14352}=\sqrt{16*897}=\sqrt{16}*\sqrt{897}=4\sqrt{897}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-4\sqrt{897}}{2*6}=\frac{-120-4\sqrt{897}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+4\sqrt{897}}{2*6}=\frac{-120+4\sqrt{897}}{12}
$