2(3-x2)+9=5x

Solution for 2(3-x2)+9=5x equation:

2(3-x2)+9=5x

We move all terms to the left:

2(3-x2)+9-(5x)=0

We add all the numbers together, and all the variables

2(-1x^2+3)-5x+9=0

We multiply parentheses

-2x^2-5x+6+9=0

We add all the numbers together, and all the variables

-2x^2-5x+15=0

a = -2; b = -5; c = +15;
Δ = b2-4ac
Δ = -52-4·(-2)·15
Δ = 145
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{-(-5)-\sqrt{145}}{2*-2}=\frac{5-\sqrt{145}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{145}}{2*-2}=\frac{5+\sqrt{145}}{-4}
$