F(x)=2x^2+7x-8

Solution for F(x)=2x^2+7x-8 equation:

(F)=2F^2+7F-8

We move all terms to the left:

(F)-(2F^2+7F-8)=0

We get rid of parentheses

-2F^2+F-7F+8=0

We add all the numbers together, and all the variables

-2F^2-6F+8=0

a = -2; b = -6; c = +8;
Δ = b2-4ac
Δ = -62-4·(-2)·8
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*-2}=\frac{-4}{-4}
=1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*-2}=\frac{16}{-4}
=-4
$