x=(7x-30)(6x-10)

Solution for x=(7x-30)(6x-10) equation:

x=(7x-30)(6x-10)

We move all terms to the left:

x-((7x-30)(6x-10))=0

We multiply parentheses ..

-((+42x^2-70x-180x+300))+x=0


We calculate terms in parentheses: -((+42x^2-70x-180x+300)), so:

(+42x^2-70x-180x+300)

We get rid of parentheses

42x^2-70x-180x+300

We add all the numbers together, and all the variables

42x^2-250x+300

Back to the equation:

-(42x^2-250x+300)


We add all the numbers together, and all the variables

x-(42x^2-250x+300)=0

We get rid of parentheses

-42x^2+x+250x-300=0

We add all the numbers together, and all the variables

-42x^2+251x-300=0

a = -42; b = 251; c = -300;
Δ = b2-4ac
Δ = 2512-4·(-42)·(-300)
Δ = 12601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(251)-\sqrt{12601}}{2*-42}=\frac{-251-\sqrt{12601}}{-84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(251)+\sqrt{12601}}{2*-42}=\frac{-251+\sqrt{12601}}{-84}
$