3x^2-5x+3=65

Solution for 3x^2-5x+3=65 equation:

3x^2-5x+3=65

We move all terms to the left:

3x^2-5x+3-(65)=0

We add all the numbers together, and all the variables

3x^2-5x-62=0

a = 3; b = -5; c = -62;
Δ = b2-4ac
Δ = -52-4·3·(-62)
Δ = 769
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{769}}{2*3}=\frac{5-\sqrt{769}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{769}}{2*3}=\frac{5+\sqrt{769}}{6}
$