29x-3x^2=46

Solution for 29x-3x^2=46 equation:

29x-3x^2=46

We move all terms to the left:

29x-3x^2-(46)=0

a = -3; b = 29; c = -46;
Δ = b2-4ac
Δ = 292-4·(-3)·(-46)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-17}{2*-3}=\frac{-46}{-6}
=7+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+17}{2*-3}=\frac{-12}{-6}
=+2
$