3(2x^2-3)=5x

Solution for 3(2x^2-3)=5x equation:

3(2x^2-3)=5x

We move all terms to the left:

3(2x^2-3)-(5x)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

6x^2-5x-9=0

a = 6; b = -5; c = -9;
Δ = b2-4ac
Δ = -52-4·6·(-9)
Δ = 241
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{-(-5)-\sqrt{241}}{2*6}=\frac{5-\sqrt{241}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{241}}{2*6}=\frac{5+\sqrt{241}}{12}
$