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x(x+7)=2x(x+2)
We move all terms to the left:
x(x+7)-(2x(x+2))=0
We multiply parentheses
x^2+7x-(2x(x+2))=0
We calculate terms in parentheses: -(2x(x+2)), so:We get rid of parentheses
2x(x+2)
We multiply parentheses
2x^2+4x
Back to the equation:
-(2x^2+4x)
x^2-2x^2+7x-4x=0
We add all the numbers together, and all the variables
-1x^2+3x=0
a = -1; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-1)·0
Δ = 9
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{9}=3$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-1}=\frac{-6}{-2} =+3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-1}=\frac{0}{-2} =0 $
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