(2x)(x+3)=105

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

(2x)(x+3)=105

We move all terms to the left:

(2x)(x+3)-(105)=0

We multiply parentheses

2x^2+6x-105=0

a = 2; b = 6; c = -105;
Δ = b2-4ac
Δ = 62-4·2·(-105)
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{219}}{2*2}=\frac{-6-2\sqrt{219}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{219}}{2*2}=\frac{-6+2\sqrt{219}}{4}
$