F(x)=x^2-36/25

Solution for F(x)=x^2-36/25 equation:

(F)=F^2-36/25

We move all terms to the left:

(F)-(F^2-36/25)=0

We get rid of parentheses

-F^2+F+36/25=0

We multiply all the terms by the denominator


-F^2*25+F*25+36=0

Wy multiply elements

-25F^2+25F+36=0

a = -25; b = 25; c = +36;
Δ = b2-4ac
Δ = 252-4·(-25)·36
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-65}{2*-25}=\frac{-90}{-50}
=1+4/5
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+65}{2*-25}=\frac{40}{-50}
=-4/5
$