x+7x^2=456

Solution for x+7x^2=456 equation:

x+7x^2=456

We move all terms to the left:

x+7x^2-(456)=0

a = 7; b = 1; c = -456;
Δ = b2-4ac
Δ = 12-4·7·(-456)
Δ = 12769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12769}=113$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-113}{2*7}=\frac{-114}{14}
=-8+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+113}{2*7}=\frac{112}{14}
=8
$