-3x^2-5x=-1

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

-3x^2-5x=-1

We move all terms to the left:

-3x^2-5x-(-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}
$