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12x=-8x(10-x)
We move all terms to the left:
12x-(-8x(10-x))=0
We add all the numbers together, and all the variables
12x-(-8x(-1x+10))=0
We calculate terms in parentheses: -(-8x(-1x+10)), so:We get rid of parentheses
-8x(-1x+10)
We multiply parentheses
8x^2-80x
Back to the equation:
-(8x^2-80x)
-8x^2+12x+80x=0
We add all the numbers together, and all the variables
-8x^2+92x=0
a = -8; b = 92; c = 0;
Δ = b2-4ac
Δ = 922-4·(-8)·0
Δ = 8464
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{8464}=92$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-92}{2*-8}=\frac{-184}{-16} =11+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+92}{2*-8}=\frac{0}{-16} =0 $
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