F(x)=x2+7x-30

Solution for F(x)=x2+7x-30 equation:

(F)=F2+7F-30

We move all terms to the left:

(F)-(F2+7F-30)=0

We add all the numbers together, and all the variables

-(+F^2+7F-30)+F=0

We get rid of parentheses

-F^2-7F+F+30=0

We add all the numbers together, and all the variables

-1F^2-6F+30=0

a = -1; b = -6; c = +30;
Δ = b2-4ac
Δ = -62-4·(-1)·30
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*-1}=\frac{6-2\sqrt{39}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*-1}=\frac{6+2\sqrt{39}}{-2}
$