(9-2x)=(7-4x+6x^2)

Solution for (9-2x)=(7-4x+6x^2) equation:

(9-2x)=(7-4x+6x^2)

We move all terms to the left:

(9-2x)-((7-4x+6x^2))=0

We add all the numbers together, and all the variables

-((7-4x+6x^2))+(-2x+9)=0

We get rid of parentheses

-((7-4x+6x^2))-2x+9=0


We calculate terms in parentheses: -((7-4x+6x^2)), so:

(7-4x+6x^2)

We get rid of parentheses

6x^2-4x+7

Back to the equation:

-(6x^2-4x+7)


We add all the numbers together, and all the variables

-2x-(6x^2-4x+7)+9=0

We get rid of parentheses

-6x^2-2x+4x-7+9=0

We add all the numbers together, and all the variables

-6x^2+2x+2=0

a = -6; b = 2; c = +2;
Δ = b2-4ac
Δ = 22-4·(-6)·2
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{13}}{2*-6}=\frac{-2-2\sqrt{13}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{13}}{2*-6}=\frac{-2+2\sqrt{13}}{-12}
$