x(3x+5)=50

Solution for x(3x+5)=50 equation:

x(3x+5)=50

We move all terms to the left:

x(3x+5)-(50)=0

We multiply parentheses

3x^2+5x-50=0

a = 3; b = 5; c = -50;
Δ = b2-4ac
Δ = 52-4·3·(-50)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-25}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+25}{2*3}=\frac{20}{6}
=3+1/3
$