48x-16=3x^2-x^2

Solution for 48x-16=3x^2-x^2 equation:

48x-16=3x^2-x^2

We move all terms to the left:

48x-16-(3x^2-x^2)=0

We get rid of parentheses

-3x^2+x^2+48x-16=0

We add all the numbers together, and all the variables

-2x^2+48x-16=0

a = -2; b = 48; c = -16;
Δ = b2-4ac
Δ = 482-4·(-2)·(-16)
Δ = 2176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{34}}{2*-2}=\frac{-48-8\sqrt{34}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{34}}{2*-2}=\frac{-48+8\sqrt{34}}{-4}
$