3x(2x+5)=10

Solution for 3x(2x+5)=10 equation:

3x(2x+5)=10

We move all terms to the left:

3x(2x+5)-(10)=0

We multiply parentheses

6x^2+15x-10=0

a = 6; b = 15; c = -10;
Δ = b2-4ac
Δ = 152-4·6·(-10)
Δ = 465
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{465}}{2*6}=\frac{-15-\sqrt{465}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{465}}{2*6}=\frac{-15+\sqrt{465}}{12}
$