5x=1-3x^2

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

5x=1-3x^2

We move all terms to the left:

5x-(1-3x^2)=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}
$