10x^2=18-9x

Solution for 10x^2=18-9x equation:

10x^2=18-9x

We move all terms to the left:

10x^2-(18-9x)=0

We add all the numbers together, and all the variables

10x^2-(-9x+18)=0

We get rid of parentheses

10x^2+9x-18=0

a = 10; b = 9; c = -18;
Δ = b2-4ac
Δ = 92-4·10·(-18)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{89}}{2*10}=\frac{-9-3\sqrt{89}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{89}}{2*10}=\frac{-9+3\sqrt{89}}{20}
$