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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-3x(-1x+4)-(2(x-5))=0

We multiply parentheses

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


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

2(x-5)

We multiply parentheses

2x-10

Back to the equation:

-(2x-10)


We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-14x+10=0

a = 3; b = -14; c = +10;
Δ = b2-4ac
Δ = -142-4·3·10
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{19}}{2*3}=\frac{14-2\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{19}}{2*3}=\frac{14+2\sqrt{19}}{6}
$