5x^2+3x^2-16x^2+48x=2

Solution for 5x^2+3x^2-16x^2+48x=2 equation:

5x^2+3x^2-16x^2+48x=2

We move all terms to the left:

5x^2+3x^2-16x^2+48x-(2)=0

We add all the numbers together, and all the variables

-8x^2+48x-2=0

a = -8; b = 48; c = -2;
Δ = b2-4ac
Δ = 482-4·(-8)·(-2)
Δ = 2240
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:

$\sqrt{\Delta}=\sqrt{2240}=\sqrt{64*35}=\sqrt{64}*\sqrt{35}=8\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{35}}{2*-8}=\frac{-48-8\sqrt{35}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{35}}{2*-8}=\frac{-48+8\sqrt{35}}{-16}
$