3x(5x+3)/6=8

Solution for 3x(5x+3)/6=8 equation:

3x(5x+3)/6=8

We move all terms to the left:

3x(5x+3)/6-(8)=0

We multiply all the terms by the denominator


3x(5x+3)-8*6=0

We add all the numbers together, and all the variables

3x(5x+3)-48=0

We multiply parentheses

15x^2+9x-48=0

a = 15; b = 9; c = -48;
Δ = b2-4ac
Δ = 92-4·15·(-48)
Δ = 2961
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:

$\sqrt{\Delta}=\sqrt{2961}=\sqrt{9*329}=\sqrt{9}*\sqrt{329}=3\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{329}}{2*15}=\frac{-9-3\sqrt{329}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{329}}{2*15}=\frac{-9+3\sqrt{329}}{30}
$