3q^2+5q=1

Solution for 3q^2+5q=1 equation:

3q^2+5q=1

We move all terms to the left:

3q^2+5q-(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:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{37}}{2*3}=\frac{-5-\sqrt{37}}{6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{37}}{2*3}=\frac{-5+\sqrt{37}}{6}
$