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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

Wy multiply elements

-30x^2-(8x+12)+78=0

We get rid of parentheses

-30x^2-8x-12+78=0

We add all the numbers together, and all the variables

-30x^2-8x+66=0

a = -30; b = -8; c = +66;
Δ = b2-4ac
Δ = -82-4·(-30)·66
Δ = 7984
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:

$\sqrt{\Delta}=\sqrt{7984}=\sqrt{16*499}=\sqrt{16}*\sqrt{499}=4\sqrt{499}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{499}}{2*-30}=\frac{8-4\sqrt{499}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{499}}{2*-30}=\frac{8+4\sqrt{499}}{-60}
$