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5x=(15.84-x)(1+x)
We move all terms to the left:
5x-((15.84-x)(1+x))=0
We add all the numbers together, and all the variables
5x-((-1x+15.84)(x+1))=0
We multiply parentheses ..
-((-1x^2-1x+15.84x+15.84))+5x=0
We calculate terms in parentheses: -((-1x^2-1x+15.84x+15.84)), so:We get rid of parentheses
(-1x^2-1x+15.84x+15.84)
We get rid of parentheses
-1x^2-1x+15.84x+15.84
We add all the numbers together, and all the variables
-1x^2+14.84x+15.84
Back to the equation:
-(-1x^2+14.84x+15.84)
1x^2-14.84x+5x-15.84=0
We add all the numbers together, and all the variables
x^2-9.84x-15.84=0
a = 1; b = -9.84; c = -15.84;
Δ = b2-4ac
Δ = -9.842-4·1·(-15.84)
Δ = 160.1856
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{-(-9.84)-\sqrt{160.1856}}{2*1}=\frac{9.84-\sqrt{160.1856}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9.84)+\sqrt{160.1856}}{2*1}=\frac{9.84+\sqrt{160.1856}}{2} $
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