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

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

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

We move all terms to the left:

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

We multiply parentheses

6x^2+10x-(5x(10x-3))=0


We calculate terms in parentheses: -(5x(10x-3)), so:

5x(10x-3)

We multiply parentheses

50x^2-15x

Back to the equation:

-(50x^2-15x)


We get rid of parentheses

6x^2-50x^2+10x+15x=0

We add all the numbers together, and all the variables

-44x^2+25x=0

a = -44; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-44)·0
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{-(25)-25}{2*-44}=\frac{-50}{-88}
=25/44
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-44}=\frac{0}{-88}
=0
$