P(x)=2x^2-8/91

Solution for P(x)=2x^2-8/91 equation:

(P)=2P^2-8/91

We move all terms to the left:

(P)-(2P^2-8/91)=0

We get rid of parentheses

-2P^2+P+8/91=0

We multiply all the terms by the denominator


-2P^2*91+P*91+8=0

Wy multiply elements

-182P^2+91P+8=0

a = -182; b = 91; c = +8;
Δ = b2-4ac
Δ = 912-4·(-182)·8
Δ = 14105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(91)-\sqrt{14105}}{2*-182}=\frac{-91-\sqrt{14105}}{-364}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+\sqrt{14105}}{2*-182}=\frac{-91+\sqrt{14105}}{-364}
$