3(x+4)=2(x-5)x

Solution for 3(x+4)=2(x-5)x equation:

3(x+4)=2(x-5)x

We move all terms to the left:

3(x+4)-(2(x-5)x)=0

We multiply parentheses

3x-(2(x-5)x)+12=0


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

2(x-5)x

We multiply parentheses

2x^2-10x

Back to the equation:

-(2x^2-10x)


We get rid of parentheses

-2x^2+3x+10x+12=0

We add all the numbers together, and all the variables

-2x^2+13x+12=0

a = -2; b = 13; c = +12;
Δ = b2-4ac
Δ = 132-4·(-2)·12
Δ = 265
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{-(13)-\sqrt{265}}{2*-2}=\frac{-13-\sqrt{265}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{265}}{2*-2}=\frac{-13+\sqrt{265}}{-4}
$