3x(5-x)=2(7-4x)

Solution for 3x(5-x)=2(7-4x) equation:

3x(5-x)=2(7-4x)

We move all terms to the left:

3x(5-x)-(2(7-4x))=0

We add all the numbers together, and all the variables

3x(-1x+5)-(2(-4x+7))=0

We multiply parentheses

-3x^2+15x-(2(-4x+7))=0


We calculate terms in parentheses: -(2(-4x+7)), so:

2(-4x+7)

We multiply parentheses

-8x+14

Back to the equation:

-(-8x+14)


We get rid of parentheses

-3x^2+15x+8x-14=0

We add all the numbers together, and all the variables

-3x^2+23x-14=0

a = -3; b = 23; c = -14;
Δ = b2-4ac
Δ = 232-4·(-3)·(-14)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-19}{2*-3}=\frac{-42}{-6}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+19}{2*-3}=\frac{-4}{-6}
=2/3
$