2x=5-7x^2

Solution for 2x=5-7x^2 equation:

2x=5-7x^2

We move all terms to the left:

2x-(5-7x^2)=0

We get rid of parentheses

7x^2+2x-5=0

a = 7; b = 2; c = -5;
Δ = b2-4ac
Δ = 22-4·7·(-5)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-12}{2*7}=\frac{-14}{14}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+12}{2*7}=\frac{10}{14}
=5/7
$