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.15x+.3x(12-x)=12(.24)
We move all terms to the left:
.15x+.3x(12-x)-(12(.24))=0
We add all the numbers together, and all the variables
.15x+.3x(-1x+12)-(12(0.24))=0
We add all the numbers together, and all the variables
.15x+.3x(-1x+12)-2.88=0
We multiply parentheses
-1x^2+.15x+12x-2.88=0
We add all the numbers together, and all the variables
-1x^2+12.15x-2.88=0
a = -1; b = 12.15; c = -2.88;
Δ = b2-4ac
Δ = 12.152-4·(-1)·(-2.88)
Δ = 136.1025
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{-(12.15)-\sqrt{136.1025}}{2*-1}=\frac{-12.15-\sqrt{136.1025}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12.15)+\sqrt{136.1025}}{2*-1}=\frac{-12.15+\sqrt{136.1025}}{-2} $
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