F(x)=-7(x+2)(5x-15)

Solution for F(x)=-7(x+2)(5x-15) equation:

(F)=-7(F+2)(5F-15)

We move all terms to the left:

(F)-(-7(F+2)(5F-15))=0

We multiply parentheses ..

-(-7(+5F^2-15F+10F-30))+F=0


We calculate terms in parentheses: -(-7(+5F^2-15F+10F-30)), so:

-7(+5F^2-15F+10F-30)

We multiply parentheses

-35F^2+105F-70F+210

We add all the numbers together, and all the variables

-35F^2+35F+210

Back to the equation:

-(-35F^2+35F+210)


We get rid of parentheses

35F^2-35F+F-210=0

We add all the numbers together, and all the variables

35F^2-34F-210=0

a = 35; b = -34; c = -210;
Δ = b2-4ac
Δ = -342-4·35·(-210)
Δ = 30556
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:

$\sqrt{\Delta}=\sqrt{30556}=\sqrt{4*7639}=\sqrt{4}*\sqrt{7639}=2\sqrt{7639}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{7639}}{2*35}=\frac{34-2\sqrt{7639}}{70}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{7639}}{2*35}=\frac{34+2\sqrt{7639}}{70}
$