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-3x+5x(x+2)=23
We move all terms to the left:
-3x+5x(x+2)-(23)=0
We multiply parentheses
5x^2-3x+10x-23=0
We add all the numbers together, and all the variables
5x^2+7x-23=0
a = 5; b = 7; c = -23;
Δ = b2-4ac
Δ = 72-4·5·(-23)
Δ = 509
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{-(7)-\sqrt{509}}{2*5}=\frac{-7-\sqrt{509}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{509}}{2*5}=\frac{-7+\sqrt{509}}{10} $
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