3x^2+22x=574

Solution for 3x^2+22x=574 equation:

3x^2+22x=574

We move all terms to the left:

3x^2+22x-(574)=0

a = 3; b = 22; c = -574;
Δ = b2-4ac
Δ = 222-4·3·(-574)
Δ = 7372
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:

$\sqrt{\Delta}=\sqrt{7372}=\sqrt{4*1843}=\sqrt{4}*\sqrt{1843}=2\sqrt{1843}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{1843}}{2*3}=\frac{-22-2\sqrt{1843}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{1843}}{2*3}=\frac{-22+2\sqrt{1843}}{6}
$