3X(2x+1)=105

Solution for 3X(2x+1)=105 equation:

3X(2X+1)=105

We move all terms to the left:

3X(2X+1)-(105)=0

We multiply parentheses

6X^2+3X-105=0

a = 6; b = 3; c = -105;
Δ = b2-4ac
Δ = 32-4·6·(-105)
Δ = 2529
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:

$\sqrt{\Delta}=\sqrt{2529}=\sqrt{9*281}=\sqrt{9}*\sqrt{281}=3\sqrt{281}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{281}}{2*6}=\frac{-3-3\sqrt{281}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{281}}{2*6}=\frac{-3+3\sqrt{281}}{12}
$