x=(5x+42)(8x-15)

Solution for x=(5x+42)(8x-15) equation:

x=(5x+42)(8x-15)

We move all terms to the left:

x-((5x+42)(8x-15))=0

We multiply parentheses ..

-((+40x^2-75x+336x-630))+x=0


We calculate terms in parentheses: -((+40x^2-75x+336x-630)), so:

(+40x^2-75x+336x-630)

We get rid of parentheses

40x^2-75x+336x-630

We add all the numbers together, and all the variables

40x^2+261x-630

Back to the equation:

-(40x^2+261x-630)


We add all the numbers together, and all the variables

x-(40x^2+261x-630)=0

We get rid of parentheses

-40x^2+x-261x+630=0

We add all the numbers together, and all the variables

-40x^2-260x+630=0

a = -40; b = -260; c = +630;
Δ = b2-4ac
Δ = -2602-4·(-40)·630
Δ = 168400
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:

$\sqrt{\Delta}=\sqrt{168400}=\sqrt{400*421}=\sqrt{400}*\sqrt{421}=20\sqrt{421}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-260)-20\sqrt{421}}{2*-40}=\frac{260-20\sqrt{421}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-260)+20\sqrt{421}}{2*-40}=\frac{260+20\sqrt{421}}{-80}
$