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5x(x-2)+1=2x-9+3x
We move all terms to the left:
5x(x-2)+1-(2x-9+3x)=0
We add all the numbers together, and all the variables
5x(x-2)-(5x-9)+1=0
We multiply parentheses
5x^2-10x-(5x-9)+1=0
We get rid of parentheses
5x^2-10x-5x+9+1=0
We add all the numbers together, and all the variables
5x^2-15x+10=0
a = 5; b = -15; c = +10;
Δ = b2-4ac
Δ = -152-4·5·10
Δ = 25
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{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5}{2*5}=\frac{10}{10} =1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5}{2*5}=\frac{20}{10} =2 $
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