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/3x-12=-4x+23
We move all terms to the left:
/3x-12-(-4x+23)=0
Domain of the equation: 3x!=0We get rid of parentheses
x!=0/3
x!=0
x∈R
/3x+4x-23-12=0
We multiply all the terms by the denominator
4x*3x-23*3x-12*3x+=0
We add all the numbers together, and all the variables
4x*3x-23*3x-12*3x=0
Wy multiply elements
12x^2-69x-36x=0
We add all the numbers together, and all the variables
12x^2-105x=0
a = 12; b = -105; c = 0;
Δ = b2-4ac
Δ = -1052-4·12·0
Δ = 11025
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{11025}=105$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-105}{2*12}=\frac{0}{24} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+105}{2*12}=\frac{210}{24} =8+3/4 $
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