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5x(x+3)=2x+21
We move all terms to the left:
5x(x+3)-(2x+21)=0
We multiply parentheses
5x^2+15x-(2x+21)=0
We get rid of parentheses
5x^2+15x-2x-21=0
We add all the numbers together, and all the variables
5x^2+13x-21=0
a = 5; b = 13; c = -21;
Δ = b2-4ac
Δ = 132-4·5·(-21)
Δ = 589
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{-(13)-\sqrt{589}}{2*5}=\frac{-13-\sqrt{589}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{589}}{2*5}=\frac{-13+\sqrt{589}}{10} $
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