3x(x-5)=22

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

3x(x-5)=22

We move all terms to the left:

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

We multiply parentheses

3x^2-15x-22=0

a = 3; b = -15; c = -22;
Δ = b2-4ac
Δ = -152-4·3·(-22)
Δ = 489
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{-(-15)-\sqrt{489}}{2*3}=\frac{15-\sqrt{489}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{489}}{2*3}=\frac{15+\sqrt{489}}{6}
$