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5x^2-x=2/3
We move all terms to the left:
5x^2-x-(2/3)=0
We add all the numbers together, and all the variables
5x^2-x-(+2/3)=0
We add all the numbers together, and all the variables
5x^2-1x-(+2/3)=0
We get rid of parentheses
5x^2-1x-2/3=0
We multiply all the terms by the denominator
5x^2*3-1x*3-2=0
Wy multiply elements
15x^2-3x-2=0
a = 15; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·15·(-2)
Δ = 129
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{129}}{2*15}=\frac{3-\sqrt{129}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{129}}{2*15}=\frac{3+\sqrt{129}}{30} $
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