(7x)=(12x+20)(20x-35)

Solution for (7x)=(12x+20)(20x-35) equation:

(7x)=(12x+20)(20x-35)

We move all terms to the left:

(7x)-((12x+20)(20x-35))=0

We multiply parentheses ..

-((+240x^2-420x+400x-700))+7x=0


We calculate terms in parentheses: -((+240x^2-420x+400x-700)), so:

(+240x^2-420x+400x-700)

We get rid of parentheses

240x^2-420x+400x-700

We add all the numbers together, and all the variables

240x^2-20x-700

Back to the equation:

-(240x^2-20x-700)


We add all the numbers together, and all the variables

7x-(240x^2-20x-700)=0

We get rid of parentheses

-240x^2+7x+20x+700=0

We add all the numbers together, and all the variables

-240x^2+27x+700=0

a = -240; b = 27; c = +700;
Δ = b2-4ac
Δ = 272-4·(-240)·700
Δ = 672729
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{-(27)-\sqrt{672729}}{2*-240}=\frac{-27-\sqrt{672729}}{-480}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{672729}}{2*-240}=\frac{-27+\sqrt{672729}}{-480}
$