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(100-x)2x=5x-7
We move all terms to the left:
(100-x)2x-(5x-7)=0
We add all the numbers together, and all the variables
(-1x+100)2x-(5x-7)=0
We multiply parentheses
-2x^2+200x-(5x-7)=0
We get rid of parentheses
-2x^2+200x-5x+7=0
We add all the numbers together, and all the variables
-2x^2+195x+7=0
a = -2; b = 195; c = +7;
Δ = b2-4ac
Δ = 1952-4·(-2)·7
Δ = 38081
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{-(195)-\sqrt{38081}}{2*-2}=\frac{-195-\sqrt{38081}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(195)+\sqrt{38081}}{2*-2}=\frac{-195+\sqrt{38081}}{-4} $
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