x+8=7x^2

Solution for x+8=7x^2 equation:

x+8=7x^2

We move all terms to the left:

x+8-(7x^2)=0

determiningTheFunctionDomain
-7x^2+x+8=0

a = -7; b = 1; c = +8;
Δ = b2-4ac
Δ = 12-4·(-7)·8
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-15}{2*-7}=\frac{-16}{-14}
=1+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+15}{2*-7}=\frac{14}{-14}
=-1
$