4x-12/3x-7=0

Solution for 4x-12/3x-7=0 equation:

4x-12/3x-7=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


4x*3x-7*3x-12=0

Wy multiply elements

12x^2-21x-12=0

a = 12; b = -21; c = -12;
Δ = b2-4ac
Δ = -212-4·12·(-12)
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{113}}{2*12}=\frac{21-3\sqrt{113}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{113}}{2*12}=\frac{21+3\sqrt{113}}{24}
$