10x^2=9x+9

Solution for 10x^2=9x+9 equation:

10x^2=9x+9

We move all terms to the left:

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

We get rid of parentheses

10x^2-9x-9=0

a = 10; b = -9; c = -9;
Δ = b2-4ac
Δ = -92-4·10·(-9)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-21}{2*10}=\frac{-12}{20}
=-3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+21}{2*10}=\frac{30}{20}
=1+1/2
$