6x2=9x-3

Solution for 6x2=9x-3 equation:

6x^2=9x-3

We move all terms to the left:

6x^2-(9x-3)=0

We get rid of parentheses

6x^2-9x+3=0

a = 6; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·6·3
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3}{2*6}=\frac{6}{12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3}{2*6}=\frac{12}{12}
=1
$