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(L)=(L+8)(8-L)
We move all terms to the left:
(L)-((L+8)(8-L))=0
We add all the numbers together, and all the variables
L-((L+8)(-1L+8))=0
We multiply parentheses ..
-((-1L^2+8L-8L+64))+L=0
We calculate terms in parentheses: -((-1L^2+8L-8L+64)), so:We get rid of parentheses
(-1L^2+8L-8L+64)
We get rid of parentheses
-1L^2+8L-8L+64
We add all the numbers together, and all the variables
-1L^2+64
Back to the equation:
-(-1L^2+64)
1L^2+L-64=0
We add all the numbers together, and all the variables
L^2+L-64=0
a = 1; b = 1; c = -64;
Δ = b2-4ac
Δ = 12-4·1·(-64)
Δ = 257
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$L_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$L_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$L_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{257}}{2*1}=\frac{-1-\sqrt{257}}{2} $$L_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{257}}{2*1}=\frac{-1+\sqrt{257}}{2} $
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