3x2=5x+1

Solution for 3x2=5x+1 equation:

3x^2=5x+1

We move all terms to the left:

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