F(x)=x^2-14x+49/15

Solution for F(x)=x^2-14x+49/15 equation:

(F)=F^2-14F+49/15

We move all terms to the left:

(F)-(F^2-14F+49/15)=0

We get rid of parentheses

-F^2+F+14F-49/15=0

We multiply all the terms by the denominator


-F^2*15+F*15+14F*15-49=0

Wy multiply elements

-15F^2+15F+210F-49=0

We add all the numbers together, and all the variables

-15F^2+225F-49=0

a = -15; b = 225; c = -49;
Δ = b2-4ac
Δ = 2252-4·(-15)·(-49)
Δ = 47685
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:

$\sqrt{\Delta}=\sqrt{47685}=\sqrt{289*165}=\sqrt{289}*\sqrt{165}=17\sqrt{165}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(225)-17\sqrt{165}}{2*-15}=\frac{-225-17\sqrt{165}}{-30}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(225)+17\sqrt{165}}{2*-15}=\frac{-225+17\sqrt{165}}{-30}
$