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

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

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

We move all terms to the left:

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

We multiply parentheses ..

-((+30x^2+48x-35x-56))+x=0


We calculate terms in parentheses: -((+30x^2+48x-35x-56)), so:

(+30x^2+48x-35x-56)

We get rid of parentheses

30x^2+48x-35x-56

We add all the numbers together, and all the variables

30x^2+13x-56

Back to the equation:

-(30x^2+13x-56)


We add all the numbers together, and all the variables

x-(30x^2+13x-56)=0

We get rid of parentheses

-30x^2+x-13x+56=0

We add all the numbers together, and all the variables

-30x^2-12x+56=0

a = -30; b = -12; c = +56;
Δ = b2-4ac
Δ = -122-4·(-30)·56
Δ = 6864
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:

$\sqrt{\Delta}=\sqrt{6864}=\sqrt{16*429}=\sqrt{16}*\sqrt{429}=4\sqrt{429}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{429}}{2*-30}=\frac{12-4\sqrt{429}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{429}}{2*-30}=\frac{12+4\sqrt{429}}{-60}
$