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(2F)=2(2F)^2+8(2F)+5
We move all terms to the left:
(2F)-(2(2F)^2+8(2F)+5)=0
We get rid of parentheses
-22F^2+2F-82F-5=0
We add all the numbers together, and all the variables
-22F^2-80F-5=0
a = -22; b = -80; c = -5;
Δ = b2-4ac
Δ = -802-4·(-22)·(-5)
Δ = 5960
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5960}=\sqrt{4*1490}=\sqrt{4}*\sqrt{1490}=2\sqrt{1490}$$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{1490}}{2*-22}=\frac{80-2\sqrt{1490}}{-44} $$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{1490}}{2*-22}=\frac{80+2\sqrt{1490}}{-44} $
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