9-3x2=2+7x

Solution for 9-3x2=2+7x equation:

9-3x^2=2+7x

We move all terms to the left:

9-3x^2-(2+7x)=0

We add all the numbers together, and all the variables

-3x^2-(7x+2)+9=0

We get rid of parentheses

-3x^2-7x-2+9=0

We add all the numbers together, and all the variables

-3x^2-7x+7=0

a = -3; b = -7; c = +7;
Δ = b2-4ac
Δ = -72-4·(-3)·7
Δ = 133
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{133}}{2*-3}=\frac{7-\sqrt{133}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{133}}{2*-3}=\frac{7+\sqrt{133}}{-6}
$