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5x(x-3)=2(x+1)
We move all terms to the left:
5x(x-3)-(2(x+1))=0
We multiply parentheses
5x^2-15x-(2(x+1))=0
We calculate terms in parentheses: -(2(x+1)), so:We get rid of parentheses
2(x+1)
We multiply parentheses
2x+2
Back to the equation:
-(2x+2)
5x^2-15x-2x-2=0
We add all the numbers together, and all the variables
5x^2-17x-2=0
a = 5; b = -17; c = -2;
Δ = b2-4ac
Δ = -172-4·5·(-2)
Δ = 329
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{-(-17)-\sqrt{329}}{2*5}=\frac{17-\sqrt{329}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{329}}{2*5}=\frac{17+\sqrt{329}}{10} $
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