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4x-12/3x-7=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
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} $
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