x(3x+5)=182

Solution for x(3x+5)=182 equation:

x(3x+5)=182

We move all terms to the left:

x(3x+5)-(182)=0

We multiply parentheses

3x^2+5x-182=0

a = 3; b = 5; c = -182;
Δ = b2-4ac
Δ = 52-4·3·(-182)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-47}{2*3}=\frac{-52}{6}
=-8+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+47}{2*3}=\frac{42}{6}
=7
$