X-3/1a=12

Solution for X-3/1a=12 equation:

X-3/1X=12

We move all terms to the left:

X-3/1X-(12)=0


Domain of the equation: 1X!=0

X∈R


We multiply all the terms by the denominator


X*1X-12*1X-3=0

Wy multiply elements

X^2-12X-3=0

a = 1; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·1·(-3)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{39}}{2*1}=\frac{12-2\sqrt{39}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{39}}{2*1}=\frac{12+2\sqrt{39}}{2}
$