2x^2+29x=105

Solution for 2x^2+29x=105 equation:

2x^2+29x=105

We move all terms to the left:

2x^2+29x-(105)=0

a = 2; b = 29; c = -105;
Δ = b2-4ac
Δ = 292-4·2·(-105)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-41}{2*2}=\frac{-70}{4}
=-17+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+41}{2*2}=\frac{12}{4}
=3
$