x=(5x+10)(7x-2)

Solution for x=(5x+10)(7x-2) equation:

x=(5x+10)(7x-2)

We move all terms to the left:

x-((5x+10)(7x-2))=0

We multiply parentheses ..

-((+35x^2-10x+70x-20))+x=0


We calculate terms in parentheses: -((+35x^2-10x+70x-20)), so:

(+35x^2-10x+70x-20)

We get rid of parentheses

35x^2-10x+70x-20

We add all the numbers together, and all the variables

35x^2+60x-20

Back to the equation:

-(35x^2+60x-20)


We add all the numbers together, and all the variables

x-(35x^2+60x-20)=0

We get rid of parentheses

-35x^2+x-60x+20=0

We add all the numbers together, and all the variables

-35x^2-59x+20=0

a = -35; b = -59; c = +20;
Δ = b2-4ac
Δ = -592-4·(-35)·20
Δ = 6281
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{-(-59)-\sqrt{6281}}{2*-35}=\frac{59-\sqrt{6281}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{6281}}{2*-35}=\frac{59+\sqrt{6281}}{-70}
$