5-x2=3x-45

Solution for 5-x2=3x-45 equation:

5-x2=3x-45

We move all terms to the left:

5-x2-(3x-45)=0

We add all the numbers together, and all the variables

-1x^2-(3x-45)+5=0

We get rid of parentheses

-1x^2-3x+45+5=0

We add all the numbers together, and all the variables

-1x^2-3x+50=0

a = -1; b = -3; c = +50;
Δ = b2-4ac
Δ = -32-4·(-1)·50
Δ = 209
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{-(-3)-\sqrt{209}}{2*-1}=\frac{3-\sqrt{209}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{209}}{2*-1}=\frac{3+\sqrt{209}}{-2}
$