(12-3/4)x=1

Solution for (12-3/4)x=1 equation:

(12-3/4)x=1

We move all terms to the left:

(12-3/4)x-(1)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(-3/4+12)x-1=0

We multiply parentheses

-3x^2+12x-1=0

a = -3; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·(-3)·(-1)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{33}}{2*-3}=\frac{-12-2\sqrt{33}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{33}}{2*-3}=\frac{-12+2\sqrt{33}}{-6}
$