1-3x^2=-5x

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

1-3x^2=-5x

We move all terms to the left:

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

We get rid of parentheses

-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}
$