F1+2f2=152

Solution for F1+2f2=152 equation:

1+2F^2=152

We move all terms to the left:

1+2F^2-(152)=0

We add all the numbers together, and all the variables

2F^2-151=0

a = 2; b = 0; c = -151;
Δ = b2-4ac
Δ = 02-4·2·(-151)
Δ = 1208
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:

$\sqrt{\Delta}=\sqrt{1208}=\sqrt{4*302}=\sqrt{4}*\sqrt{302}=2\sqrt{302}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{302}}{2*2}=\frac{0-2\sqrt{302}}{4}
=-\frac{2\sqrt{302}}{4}
=-\frac{\sqrt{302}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{302}}{2*2}=\frac{0+2\sqrt{302}}{4}
=\frac{2\sqrt{302}}{4}
=\frac{\sqrt{302}}{2}
$