6x(3x+5)=10

Solution for 6x(3x+5)=10 equation:

6x(3x+5)=10

We move all terms to the left:

6x(3x+5)-(10)=0

We multiply parentheses

18x^2+30x-10=0

a = 18; b = 30; c = -10;
Δ = b2-4ac
Δ = 302-4·18·(-10)
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-18\sqrt{5}}{2*18}=\frac{-30-18\sqrt{5}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+18\sqrt{5}}{2*18}=\frac{-30+18\sqrt{5}}{36}
$