(4x^2-26x+12)/(x-6)=0

Solution for (4x^2-26x+12)/(x-6)=0 equation:

(4x^2-26x+12)/(x-6)=0


Domain of the equation: (x-6)!=0

We move all terms containing x to the left, all other terms to the right

x!=6

x∈R


We multiply all the terms by the denominator


(4x^2-26x+12)=0

We get rid of parentheses

4x^2-26x+12=0

a = 4; b = -26; c = +12;
Δ = b2-4ac
Δ = -262-4·4·12
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-22}{2*4}=\frac{4}{8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+22}{2*4}=\frac{48}{8}
=6
$