x(2x+3)=434

Solution for x(2x+3)=434 equation:

x(2x+3)=434

We move all terms to the left:

x(2x+3)-(434)=0

We multiply parentheses

2x^2+3x-434=0

a = 2; b = 3; c = -434;
Δ = b2-4ac
Δ = 32-4·2·(-434)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-59}{2*2}=\frac{-62}{4}
=-15+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+59}{2*2}=\frac{56}{4}
=14
$