-3x=5-7x^2

Solution for -3x=5-7x^2 equation:

-3x=5-7x^2

We move all terms to the left:

-3x-(5-7x^2)=0

We get rid of parentheses

7x^2-3x-5=0

a = 7; b = -3; c = -5;
Δ = b2-4ac
Δ = -32-4·7·(-5)
Δ = 149
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{149}}{2*7}=\frac{3-\sqrt{149}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{149}}{2*7}=\frac{3+\sqrt{149}}{14}
$