5x2-3x+2=65

Solution for 5x2-3x+2=65 equation:

5x^2-3x+2=65

We move all terms to the left:

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

We add all the numbers together, and all the variables

5x^2-3x-63=0

a = 5; b = -3; c = -63;
Δ = b2-4ac
Δ = -32-4·5·(-63)
Δ = 1269
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1269}=\sqrt{9*141}=\sqrt{9}*\sqrt{141}=3\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{141}}{2*5}=\frac{3-3\sqrt{141}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{141}}{2*5}=\frac{3+3\sqrt{141}}{10}
$