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-2(3x-5)=9/2x-2
We move all terms to the left:
-2(3x-5)-(9/2x-2)=0
Domain of the equation: 2x-2)!=0We multiply parentheses
x∈R
-6x-(9/2x-2)+10=0
We get rid of parentheses
-6x-9/2x+2+10=0
We multiply all the terms by the denominator
-6x*2x+2*2x+10*2x-9=0
Wy multiply elements
-12x^2+4x+20x-9=0
We add all the numbers together, and all the variables
-12x^2+24x-9=0
a = -12; b = 24; c = -9;
Δ = b2-4ac
Δ = 242-4·(-12)·(-9)
Δ = 144
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{144}=12x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12}{2*-12}=\frac{-36}{-24} =1+1/2x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12}{2*-12}=\frac{-12}{-24} =1/2
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