3x-85=1/2x+20

Solution for 3x-85=1/2x+20 equation:

3x-85=1/2x+20

We move all terms to the left:

3x-85-(1/2x+20)=0


Domain of the equation: 2x+20)!=0

x∈R


We get rid of parentheses

3x-1/2x-20-85=0

We multiply all the terms by the denominator


3x*2x-20*2x-85*2x-1=0

Wy multiply elements

6x^2-40x-170x-1=0

We add all the numbers together, and all the variables

6x^2-210x-1=0

a = 6; b = -210; c = -1;
Δ = b2-4ac
Δ = -2102-4·6·(-1)
Δ = 44124
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:

$\sqrt{\Delta}=\sqrt{44124}=\sqrt{4*11031}=\sqrt{4}*\sqrt{11031}=2\sqrt{11031}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-2\sqrt{11031}}{2*6}=\frac{210-2\sqrt{11031}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+2\sqrt{11031}}{2*6}=\frac{210+2\sqrt{11031}}{12}
$