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.3x+.5x(50-x)=18
We move all terms to the left:
.3x+.5x(50-x)-(18)=0
We add all the numbers together, and all the variables
.3x+.5x(-1x+50)-18=0
We multiply parentheses
-1x^2+.3x+50x-18=0
We add all the numbers together, and all the variables
-1x^2+50.3x-18=0
a = -1; b = 50.3; c = -18;
Δ = b2-4ac
Δ = 50.32-4·(-1)·(-18)
Δ = 2458.09
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{-(50.3)-\sqrt{2458.09}}{2*-1}=\frac{-50.3-\sqrt{2458.09}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50.3)+\sqrt{2458.09}}{2*-1}=\frac{-50.3+\sqrt{2458.09}}{-2} $
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