F(x)=2x^2+10x-7

Solution for F(x)=2x^2+10x-7 equation:

(F)=2F^2+10F-7

We move all terms to the left:

(F)-(2F^2+10F-7)=0

We get rid of parentheses

-2F^2+F-10F+7=0

We add all the numbers together, and all the variables

-2F^2-9F+7=0

a = -2; b = -9; c = +7;
Δ = b2-4ac
Δ = -92-4·(-2)·7
Δ = 137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{137}}{2*-2}=\frac{9-\sqrt{137}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{137}}{2*-2}=\frac{9+\sqrt{137}}{-4}
$