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.5x+.1x(48-x)=14.4
We move all terms to the left:
.5x+.1x(48-x)-(14.4)=0
We add all the numbers together, and all the variables
.5x+.1x(-1x+48)-(14.4)=0
We add all the numbers together, and all the variables
.5x+.1x(-1x+48)-14.4=0
We multiply parentheses
-1x^2+.5x+48x-14.4=0
We add all the numbers together, and all the variables
-1x^2+48.5x-14.4=0
a = -1; b = 48.5; c = -14.4;
Δ = b2-4ac
Δ = 48.52-4·(-1)·(-14.4)
Δ = 2294.65
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{-(48.5)-\sqrt{2294.65}}{2*-1}=\frac{-48.5-\sqrt{2294.65}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48.5)+\sqrt{2294.65}}{2*-1}=\frac{-48.5+\sqrt{2294.65}}{-2} $
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