-9x=-39+x+5x^2

Solution for -9x=-39+x+5x^2 equation:

-9x=-39+x+5x^2

We move all terms to the left:

-9x-(-39+x+5x^2)=0

We get rid of parentheses

-5x^2-x-9x+39=0

We add all the numbers together, and all the variables

-5x^2-10x+39=0

a = -5; b = -10; c = +39;
Δ = b2-4ac
Δ = -102-4·(-5)·39
Δ = 880
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{55}}{2*-5}=\frac{10-4\sqrt{55}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{55}}{2*-5}=\frac{10+4\sqrt{55}}{-10}
$