X-3/2y=12

Solution for X-3/2y=12 equation:

X-3/2X=12

We move all terms to the left:

X-3/2X-(12)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-12*2X-3=0

Wy multiply elements

2X^2-24X-3=0

a = 2; b = -24; c = -3;
Δ = b2-4ac
Δ = -242-4·2·(-3)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-10\sqrt{6}}{2*2}=\frac{24-10\sqrt{6}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+10\sqrt{6}}{2*2}=\frac{24+10\sqrt{6}}{4}
$