5-3x=x2

Solution for 5-3x=x2 equation:

5-3x=x2

We move all terms to the left:

5-3x-(x2)=0

We add all the numbers together, and all the variables

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

a = -1; b = -3; c = +5;
Δ = b2-4ac
Δ = -32-4·(-1)·5
Δ = 29
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{29}}{2*-1}=\frac{3-\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{29}}{2*-1}=\frac{3+\sqrt{29}}{-2}
$