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(F)=(8F-3)(2F+7)
We move all terms to the left:
(F)-((8F-3)(2F+7))=0
We multiply parentheses ..
-((+16F^2+56F-6F-21))+F=0
We calculate terms in parentheses: -((+16F^2+56F-6F-21)), so:We add all the numbers together, and all the variables
(+16F^2+56F-6F-21)
We get rid of parentheses
16F^2+56F-6F-21
We add all the numbers together, and all the variables
16F^2+50F-21
Back to the equation:
-(16F^2+50F-21)
F-(16F^2+50F-21)=0
We get rid of parentheses
-16F^2+F-50F+21=0
We add all the numbers together, and all the variables
-16F^2-49F+21=0
a = -16; b = -49; c = +21;
Δ = b2-4ac
Δ = -492-4·(-16)·21
Δ = 3745
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}$$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-\sqrt{3745}}{2*-16}=\frac{49-\sqrt{3745}}{-32} $$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{3745}}{2*-16}=\frac{49+\sqrt{3745}}{-32} $
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