3x^2-x-173=11x+7

Solution for 3x^2-x-173=11x+7 equation:

3x^2-x-173=11x+7

We move all terms to the left:

3x^2-x-173-(11x+7)=0

We add all the numbers together, and all the variables

3x^2-1x-(11x+7)-173=0

We get rid of parentheses

3x^2-1x-11x-7-173=0

We add all the numbers together, and all the variables

3x^2-12x-180=0

a = 3; b = -12; c = -180;
Δ = b2-4ac
Δ = -122-4·3·(-180)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-48}{2*3}=\frac{-36}{6}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+48}{2*3}=\frac{60}{6}
=10
$