5x-3x^2=-1

Solution for 5x-3x^2=-1 equation:

5x-3x^2=-1

We move all terms to the left:

5x-3x^2-(-1)=0

We add all the numbers together, and all the variables

-3x^2+5x+1=0

a = -3; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·(-3)·1
Δ = 37
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{-(5)-\sqrt{37}}{2*-3}=\frac{-5-\sqrt{37}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{37}}{2*-3}=\frac{-5+\sqrt{37}}{-6}
$