3x(2x-7)=5x+2

Solution for 3x(2x-7)=5x+2 equation:

3x(2x-7)=5x+2

We move all terms to the left:

3x(2x-7)-(5x+2)=0

We multiply parentheses

6x^2-21x-(5x+2)=0

We get rid of parentheses

6x^2-21x-5x-2=0

We add all the numbers together, and all the variables

6x^2-26x-2=0

a = 6; b = -26; c = -2;
Δ = b2-4ac
Δ = -262-4·6·(-2)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{181}}{2*6}=\frac{26-2\sqrt{181}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{181}}{2*6}=\frac{26+2\sqrt{181}}{12}
$