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3-2.7x(8-x)=16.5
We move all terms to the left:
3-2.7x(8-x)-(16.5)=0
We add all the numbers together, and all the variables
-2.7x(-1x+8)+3-(16.5)=0
We add all the numbers together, and all the variables
-2.7x(-1x+8)-13.5=0
We multiply parentheses
2x^2-16x-13.5=0
a = 2; b = -16; c = -13.5;
Δ = b2-4ac
Δ = -162-4·2·(-13.5)
Δ = 364
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{91}}{2*2}=\frac{16-2\sqrt{91}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{91}}{2*2}=\frac{16+2\sqrt{91}}{4} $
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