7x^2=9-6x

Solution for 7x^2=9-6x equation:

7x^2=9-6x

We move all terms to the left:

7x^2-(9-6x)=0

We add all the numbers together, and all the variables

7x^2-(-6x+9)=0

We get rid of parentheses

7x^2+6x-9=0

a = 7; b = 6; c = -9;
Δ = b2-4ac
Δ = 62-4·7·(-9)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12\sqrt{2}}{2*7}=\frac{-6-12\sqrt{2}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12\sqrt{2}}{2*7}=\frac{-6+12\sqrt{2}}{14}
$