9x2+2=10x

Solution for 9x2+2=10x equation:

9x^2+2=10x

We move all terms to the left:

9x^2+2-(10x)=0

a = 9; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·9·2
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{7}}{2*9}=\frac{10-2\sqrt{7}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{7}}{2*9}=\frac{10+2\sqrt{7}}{18}
$