55-3x*8x+12*10x+23=0

Solution for 55-3x*8x+12*10x+23=0 equation:

55-3x*8x+12*10x+23=0

We add all the numbers together, and all the variables

-3x*8x+12*10x+78=0

Wy multiply elements

-24x^2+120x+78=0

a = -24; b = 120; c = +78;
Δ = b2-4ac
Δ = 1202-4·(-24)·78
Δ = 21888
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:

$\sqrt{\Delta}=\sqrt{21888}=\sqrt{576*38}=\sqrt{576}*\sqrt{38}=24\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-24\sqrt{38}}{2*-24}=\frac{-120-24\sqrt{38}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+24\sqrt{38}}{2*-24}=\frac{-120+24\sqrt{38}}{-48}
$