3(x+12-5)x=22

Solution for 3(x+12-5)x=22 equation:

3(x+12-5)x=22

We move all terms to the left:

3(x+12-5)x-(22)=0

We add all the numbers together, and all the variables

3(x+7)x-22=0

We multiply parentheses

3x^2+21x-22=0

a = 3; b = 21; c = -22;
Δ = b2-4ac
Δ = 212-4·3·(-22)
Δ = 705
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{705}}{2*3}=\frac{-21-\sqrt{705}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{705}}{2*3}=\frac{-21+\sqrt{705}}{6}
$