2=5x^2-16x+3

Solution for 2=5x^2-16x+3 equation:

2=5x^2-16x+3

We move all terms to the left:

2-(5x^2-16x+3)=0

We get rid of parentheses

-5x^2+16x-3+2=0

We add all the numbers together, and all the variables

-5x^2+16x-1=0

a = -5; b = 16; c = -1;
Δ = b2-4ac
Δ = 162-4·(-5)·(-1)
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{59}}{2*-5}=\frac{-16-2\sqrt{59}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{59}}{2*-5}=\frac{-16+2\sqrt{59}}{-10}
$