10x(3x+5)=6

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

10x(3x+5)=6

We move all terms to the left:

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

We multiply parentheses

30x^2+50x-6=0

a = 30; b = 50; c = -6;
Δ = b2-4ac
Δ = 502-4·30·(-6)
Δ = 3220
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:

$\sqrt{\Delta}=\sqrt{3220}=\sqrt{4*805}=\sqrt{4}*\sqrt{805}=2\sqrt{805}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{805}}{2*30}=\frac{-50-2\sqrt{805}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{805}}{2*30}=\frac{-50+2\sqrt{805}}{60}
$