3x(x+10)=52

Solution for 3x(x+10)=52 equation:

3x(x+10)=52

We move all terms to the left:

3x(x+10)-(52)=0

We multiply parentheses

3x^2+30x-52=0

a = 3; b = 30; c = -52;
Δ = b2-4ac
Δ = 302-4·3·(-52)
Δ = 1524
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1524}=\sqrt{4*381}=\sqrt{4}*\sqrt{381}=2\sqrt{381}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{381}}{2*3}=\frac{-30-2\sqrt{381}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{381}}{2*3}=\frac{-30+2\sqrt{381}}{6}
$