18x^2=14-9x

Solution for 18x^2=14-9x equation:

18x^2=14-9x

We move all terms to the left:

18x^2-(14-9x)=0

We add all the numbers together, and all the variables

18x^2-(-9x+14)=0

We get rid of parentheses

18x^2+9x-14=0

a = 18; b = 9; c = -14;
Δ = b2-4ac
Δ = 92-4·18·(-14)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-33}{2*18}=\frac{-42}{36}
=-1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+33}{2*18}=\frac{24}{36}
=2/3
$