80-6x=35-3/2x

Solution for 80-6x=35-3/2x equation:

80-6x=35-3/2x

We move all terms to the left:

80-6x-(35-3/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-6x-(-3/2x+35)+80=0

We get rid of parentheses

-6x+3/2x-35+80=0

We multiply all the terms by the denominator


-6x*2x-35*2x+80*2x+3=0

Wy multiply elements

-12x^2-70x+160x+3=0

We add all the numbers together, and all the variables

-12x^2+90x+3=0

a = -12; b = 90; c = +3;
Δ = b2-4ac
Δ = 902-4·(-12)·3
Δ = 8244
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:

$\sqrt{\Delta}=\sqrt{8244}=\sqrt{36*229}=\sqrt{36}*\sqrt{229}=6\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{229}}{2*-12}=\frac{-90-6\sqrt{229}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{229}}{2*-12}=\frac{-90+6\sqrt{229}}{-24}
$