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-10x(-4x+1)=-50x(2+x)
We move all terms to the left:
-10x(-4x+1)-(-50x(2+x))=0
We add all the numbers together, and all the variables
-10x(-4x+1)-(-50x(x+2))=0
We multiply parentheses
40x^2-10x-(-50x(x+2))=0
We calculate terms in parentheses: -(-50x(x+2)), so:We get rid of parentheses
-50x(x+2)
We multiply parentheses
-50x^2-100x
Back to the equation:
-(-50x^2-100x)
40x^2+50x^2+100x-10x=0
We add all the numbers together, and all the variables
90x^2+90x=0
a = 90; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·90·0
Δ = 8100
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{8100}=90$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*90}=\frac{-180}{180} =-1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*90}=\frac{0}{180} =0 $
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