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(F)=-7/5F-12
We move all terms to the left:
(F)-(-7/5F-12)=0
Domain of the equation: 5F-12)!=0We get rid of parentheses
F∈R
F+7/5F+12=0
We multiply all the terms by the denominator
F*5F+12*5F+7=0
Wy multiply elements
5F^2+60F+7=0
a = 5; b = 60; c = +7;
Δ = b2-4ac
Δ = 602-4·5·7
Δ = 3460
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}$$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3460}=\sqrt{4*865}=\sqrt{4}*\sqrt{865}=2\sqrt{865}$$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{865}}{2*5}=\frac{-60-2\sqrt{865}}{10} $$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{865}}{2*5}=\frac{-60+2\sqrt{865}}{10} $
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