F(x)=x+4x^2-7

Solution for F(x)=x+4x^2-7 equation:

(F)=F+4F^2-7

We move all terms to the left:

(F)-(F+4F^2-7)=0

We get rid of parentheses

-4F^2-F+F+7=0

We add all the numbers together, and all the variables

-4F^2+7=0

a = -4; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-4)·7
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*-4}=\frac{0-4\sqrt{7}}{-8}
=-\frac{4\sqrt{7}}{-8}
=-\frac{\sqrt{7}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*-4}=\frac{0+4\sqrt{7}}{-8}
=\frac{4\sqrt{7}}{-8}
=\frac{\sqrt{7}}{-2}
$