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0=4x^2-64x+192
We move all terms to the left:
0-(4x^2-64x+192)=0
We add all the numbers together, and all the variables
-(4x^2-64x+192)=0
We get rid of parentheses
-4x^2+64x-192=0
a = -4; b = 64; c = -192;
Δ = b2-4ac
Δ = 642-4·(-4)·(-192)
Δ = 1024
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1024}=32$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-32}{2*-4}=\frac{-96}{-8} =+12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+32}{2*-4}=\frac{-32}{-8} =+4 $
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