9x^2=10x-1.5

Solution for 9x^2=10x-1.5 equation:

9x^2=10x-1.5

We move all terms to the left:

9x^2-(10x-1.5)=0

We get rid of parentheses

9x^2-10x+1.5=0

a = 9; b = -10; c = +1.5;
Δ = b2-4ac
Δ = -102-4·9·1.5
Δ = 46
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{-(-10)-\sqrt{46}}{2*9}=\frac{10-\sqrt{46}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+\sqrt{46}}{2*9}=\frac{10+\sqrt{46}}{18}
$