x(2x+5)=348

Solution for x(2x+5)=348 equation:

x(2x+5)=348

We move all terms to the left:

x(2x+5)-(348)=0

We multiply parentheses

2x^2+5x-348=0

a = 2; b = 5; c = -348;
Δ = b2-4ac
Δ = 52-4·2·(-348)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-53}{2*2}=\frac{-58}{4}
=-14+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+53}{2*2}=\frac{48}{4}
=12
$