3x^2-5x=22

Solution for 3x^2-5x=22 equation:

3x^2-5x=22

We move all terms to the left:

3x^2-5x-(22)=0

a = 3; b = -5; c = -22;
Δ = b2-4ac
Δ = -52-4·3·(-22)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-17}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+17}{2*3}=\frac{22}{6}
=3+2/3
$