10(5x-4)+3(2x-1)=12x(2-3x)

Solution for 10(5x-4)+3(2x-1)=12x(2-3x) equation:

10(5x-4)+3(2x-1)=12x(2-3x)

We move all terms to the left:

10(5x-4)+3(2x-1)-(12x(2-3x))=0

We add all the numbers together, and all the variables

10(5x-4)+3(2x-1)-(12x(-3x+2))=0

We multiply parentheses

50x+6x-(12x(-3x+2))-40-3=0


We calculate terms in parentheses: -(12x(-3x+2)), so:

12x(-3x+2)

We multiply parentheses

-36x^2+24x

Back to the equation:

-(-36x^2+24x)


We add all the numbers together, and all the variables

-(-36x^2+24x)+56x-43=0

We get rid of parentheses

36x^2-24x+56x-43=0

We add all the numbers together, and all the variables

36x^2+32x-43=0

a = 36; b = 32; c = -43;
Δ = b2-4ac
Δ = 322-4·36·(-43)
Δ = 7216
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:

$\sqrt{\Delta}=\sqrt{7216}=\sqrt{16*451}=\sqrt{16}*\sqrt{451}=4\sqrt{451}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{451}}{2*36}=\frac{-32-4\sqrt{451}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{451}}{2*36}=\frac{-32+4\sqrt{451}}{72}
$