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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(3x(x-5)-2x), so:

3x(x-5)-2x

We add all the numbers together, and all the variables

-2x+3x(x-5)

We multiply parentheses

3x^2-2x-15x

We add all the numbers together, and all the variables

3x^2-17x

Back to the equation:

-(3x^2-17x)


We get rid of parentheses

-3x^2+2x+17x-10=0

We add all the numbers together, and all the variables

-3x^2+19x-10=0

a = -3; b = 19; c = -10;
Δ = b2-4ac
Δ = 192-4·(-3)·(-10)
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{-(19)-\sqrt{241}}{2*-3}=\frac{-19-\sqrt{241}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{241}}{2*-3}=\frac{-19+\sqrt{241}}{-6}
$