23x^2=16x-2

Solution for 23x^2=16x-2 equation:

23x^2=16x-2

We move all terms to the left:

23x^2-(16x-2)=0

We get rid of parentheses

23x^2-16x+2=0

a = 23; b = -16; c = +2;
Δ = b2-4ac
Δ = -162-4·23·2
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-6\sqrt{2}}{2*23}=\frac{16-6\sqrt{2}}{46}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+6\sqrt{2}}{2*23}=\frac{16+6\sqrt{2}}{46}
$