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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-3x^2-15x-(+2x-10/3)=0

We get rid of parentheses

-3x^2-15x-2x+10/3=0

We multiply all the terms by the denominator


-3x^2*3-15x*3-2x*3+10=0

Wy multiply elements

-9x^2-45x-6x+10=0

We add all the numbers together, and all the variables

-9x^2-51x+10=0

a = -9; b = -51; c = +10;
Δ = b2-4ac
Δ = -512-4·(-9)·10
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{-(-51)-3\sqrt{329}}{2*-9}=\frac{51-3\sqrt{329}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+3\sqrt{329}}{2*-9}=\frac{51+3\sqrt{329}}{-18}
$