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(2.5)=2F^2+3F+-7
We move all terms to the left:
(2.5)-(2F^2+3F+-7)=0
We add all the numbers together, and all the variables
-(2F^2+3F+-7)+2.5=0
We use the square of the difference formula
-(2F^2+3F-7)+2.5=0
We get rid of parentheses
-2F^2-3F+7+2.5=0
We add all the numbers together, and all the variables
-2F^2-3F+9.5=0
a = -2; b = -3; c = +9.5;
Δ = b2-4ac
Δ = -32-4·(-2)·9.5
Δ = 85
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{-(-3)-\sqrt{85}}{2*-2}=\frac{3-\sqrt{85}}{-4} $$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{85}}{2*-2}=\frac{3+\sqrt{85}}{-4} $
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