-3x(x-4)=-5(8x+5)

Solution for -3x(x-4)=-5(8x+5) equation:

-3x(x-4)=-5(8x+5)

We move all terms to the left:

-3x(x-4)-(-5(8x+5))=0

We multiply parentheses

-3x^2+12x-(-5(8x+5))=0


We calculate terms in parentheses: -(-5(8x+5)), so:

-5(8x+5)

We multiply parentheses

-40x-25

Back to the equation:

-(-40x-25)


We get rid of parentheses

-3x^2+12x+40x+25=0

We add all the numbers together, and all the variables

-3x^2+52x+25=0

a = -3; b = 52; c = +25;
Δ = b2-4ac
Δ = 522-4·(-3)·25
Δ = 3004
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:

$\sqrt{\Delta}=\sqrt{3004}=\sqrt{4*751}=\sqrt{4}*\sqrt{751}=2\sqrt{751}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-2\sqrt{751}}{2*-3}=\frac{-52-2\sqrt{751}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+2\sqrt{751}}{2*-3}=\frac{-52+2\sqrt{751}}{-6}
$