3x2-34x=105

Solution for 3x2-34x=105 equation:

3x^2-34x=105

We move all terms to the left:

3x^2-34x-(105)=0

a = 3; b = -34; c = -105;
Δ = b2-4ac
Δ = -342-4·3·(-105)
Δ = 2416
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:

$\sqrt{\Delta}=\sqrt{2416}=\sqrt{16*151}=\sqrt{16}*\sqrt{151}=4\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-4\sqrt{151}}{2*3}=\frac{34-4\sqrt{151}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+4\sqrt{151}}{2*3}=\frac{34+4\sqrt{151}}{6}
$