(x)(2x+1)=105

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

(x)(2x+1)=105

We move all terms to the left:

(x)(2x+1)-(105)=0

We multiply parentheses

2x^2+x-105=0

a = 2; b = 1; c = -105;
Δ = b2-4ac
Δ = 12-4·2·(-105)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-29}{2*2}=\frac{-30}{4}
=-7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+29}{2*2}=\frac{28}{4}
=7
$