3x-9x^2=-103

Solution for 3x-9x^2=-103 equation:

3x-9x^2=-103

We move all terms to the left:

3x-9x^2-(-103)=0

We add all the numbers together, and all the variables

-9x^2+3x+103=0

a = -9; b = 3; c = +103;
Δ = b2-4ac
Δ = 32-4·(-9)·103
Δ = 3717
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:

$\sqrt{\Delta}=\sqrt{3717}=\sqrt{9*413}=\sqrt{9}*\sqrt{413}=3\sqrt{413}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{413}}{2*-9}=\frac{-3-3\sqrt{413}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{413}}{2*-9}=\frac{-3+3\sqrt{413}}{-18}
$