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(100-2x)(5x-9)=0
We add all the numbers together, and all the variables
(-2x+100)(5x-9)=0
We multiply parentheses ..
(-10x^2+18x+500x-900)=0
We get rid of parentheses
-10x^2+18x+500x-900=0
We add all the numbers together, and all the variables
-10x^2+518x-900=0
a = -10; b = 518; c = -900;
Δ = b2-4ac
Δ = 5182-4·(-10)·(-900)
Δ = 232324
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{232324}=482$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(518)-482}{2*-10}=\frac{-1000}{-20} =+50 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(518)+482}{2*-10}=\frac{-36}{-20} =1+4/5 $
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