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x(18-1.2x)=22.5
We move all terms to the left:
x(18-1.2x)-(22.5)=0
We add all the numbers together, and all the variables
x(-1.2x+18)-(22.5)=0
We add all the numbers together, and all the variables
x(-1.2x+18)-22.5=0
We multiply parentheses
-1x^2+18x-22.5=0
a = -1; b = 18; c = -22.5;
Δ = b2-4ac
Δ = 182-4·(-1)·(-22.5)
Δ = 234
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{234}=\sqrt{9*26}=\sqrt{9}*\sqrt{26}=3\sqrt{26}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-3\sqrt{26}}{2*-1}=\frac{-18-3\sqrt{26}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+3\sqrt{26}}{2*-1}=\frac{-18+3\sqrt{26}}{-2} $
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