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

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

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

We move all terms to the left:

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

We multiply parentheses

-5x^2+2x+15x-(2(x-10))=0


We calculate terms in parentheses: -(2(x-10)), so:

2(x-10)

We multiply parentheses

2x-20

Back to the equation:

-(2x-20)


We add all the numbers together, and all the variables

-5x^2+17x-(2x-20)=0

We get rid of parentheses

-5x^2+17x-2x+20=0

We add all the numbers together, and all the variables

-5x^2+15x+20=0

a = -5; b = 15; c = +20;
Δ = b2-4ac
Δ = 152-4·(-5)·20
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-25}{2*-5}=\frac{-40}{-10}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+25}{2*-5}=\frac{10}{-10}
=-1
$