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

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

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

We move all terms to the left:

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

We multiply parentheses

3x-(x(2x-3))+15=0


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

x(2x-3)

We multiply parentheses

2x^2-3x

Back to the equation:

-(2x^2-3x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 6; c = +15;
Δ = b2-4ac
Δ = 62-4·(-2)·15
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{39}}{2*-2}=\frac{-6-2\sqrt{39}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{39}}{2*-2}=\frac{-6+2\sqrt{39}}{-4}
$