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/2x-5=3x+2
We move all terms to the left:
/2x-5-(3x+2)=0
Domain of the equation: 2x!=0We get rid of parentheses
x!=0/2
x!=0
x∈R
/2x-3x-2-5=0
We multiply all the terms by the denominator
-3x*2x-2*2x-5*2x+=0
We add all the numbers together, and all the variables
-3x*2x-2*2x-5*2x=0
Wy multiply elements
-6x^2-4x-10x=0
We add all the numbers together, and all the variables
-6x^2-14x=0
a = -6; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-6)·0
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*-6}=\frac{0}{-12} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-6}=\frac{28}{-12} =-2+1/3 $
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