6(2x+5)(x+4)=36(x-2)(2x+5)

Solution for 6(2x+5)(x+4)=36(x-2)(2x+5) equation:

6(2x+5)(x+4)=36(x-2)(2x+5)

We move all terms to the left:

6(2x+5)(x+4)-(36(x-2)(2x+5))=0

We multiply parentheses ..

6(+2x^2+8x+5x+20)-(36(x-2)(2x+5))=0


We calculate terms in parentheses: -(36(x-2)(2x+5)), so:

36(x-2)(2x+5)

We multiply parentheses ..

36(+2x^2+5x-4x-10)

We multiply parentheses

72x^2+180x-144x-360

We add all the numbers together, and all the variables

72x^2+36x-360

Back to the equation:

-(72x^2+36x-360)


We multiply parentheses

12x^2+48x+30x-(72x^2+36x-360)+120=0

We get rid of parentheses

12x^2-72x^2+48x+30x-36x+360+120=0

We add all the numbers together, and all the variables

-60x^2+42x+480=0

a = -60; b = 42; c = +480;
Δ = b2-4ac
Δ = 422-4·(-60)·480
Δ = 116964
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{116964}=342$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-342}{2*-60}=\frac{-384}{-120}
=3+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+342}{2*-60}=\frac{300}{-120}
=-2+1/2
$