7x(4x+5)=6x(8x+-6)

Solution for 7x(4x+5)=6x(8x+-6) equation:

7x(4x+5)=6x(8x+-6)

We move all terms to the left:

7x(4x+5)-(6x(8x+-6))=0

We add all the numbers together, and all the variables

7x(4x+5)-(6x(8x-6))=0

We multiply parentheses

28x^2+35x-(6x(8x-6))=0


We calculate terms in parentheses: -(6x(8x-6)), so:

6x(8x-6)

We multiply parentheses

48x^2-36x

Back to the equation:

-(48x^2-36x)


We get rid of parentheses

28x^2-48x^2+35x+36x=0

We add all the numbers together, and all the variables

-20x^2+71x=0

a = -20; b = 71; c = 0;
Δ = b2-4ac
Δ = 712-4·(-20)·0
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(71)-71}{2*-20}=\frac{-142}{-40}
=3+11/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(71)+71}{2*-20}=\frac{0}{-40}
=0
$