38x-3x^2=55

Solution for 38x-3x^2=55 equation:

38x-3x^2=55

We move all terms to the left:

38x-3x^2-(55)=0

a = -3; b = 38; c = -55;
Δ = b2-4ac
Δ = 382-4·(-3)·(-55)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-28}{2*-3}=\frac{-66}{-6}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+28}{2*-3}=\frac{-10}{-6}
=1+2/3
$