3/2X+8=3x-20

Solution for 3/2X+8=3x-20 equation:

3/2X+8=3X-20

We move all terms to the left:

3/2X+8-(3X-20)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We get rid of parentheses

3/2X-3X+20+8=0

We multiply all the terms by the denominator


-3X*2X+20*2X+8*2X+3=0

Wy multiply elements

-6X^2+40X+16X+3=0

We add all the numbers together, and all the variables

-6X^2+56X+3=0

a = -6; b = 56; c = +3;
Δ = b2-4ac
Δ = 562-4·(-6)·3
Δ = 3208
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:

$\sqrt{\Delta}=\sqrt{3208}=\sqrt{4*802}=\sqrt{4}*\sqrt{802}=2\sqrt{802}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{802}}{2*-6}=\frac{-56-2\sqrt{802}}{-12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{802}}{2*-6}=\frac{-56+2\sqrt{802}}{-12}
$