X-3/2x-5=1

Solution for X-3/2x-5=1 equation:

X-3/2X-5=1

We move all terms to the left:

X-3/2X-5-(1)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

X-3/2X-6=0

We multiply all the terms by the denominator


X*2X-6*2X-3=0

Wy multiply elements

2X^2-12X-3=0

a = 2; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·2·(-3)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{42}}{2*2}=\frac{12-2\sqrt{42}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{42}}{2*2}=\frac{12+2\sqrt{42}}{4}
$