-10x-7=25x(5x-7)

Solution for -10x-7=25x(5x-7) equation:

-10x-7=25x(5x-7)

We move all terms to the left:

-10x-7-(25x(5x-7))=0


We calculate terms in parentheses: -(25x(5x-7)), so:

25x(5x-7)

We multiply parentheses

125x^2-175x

Back to the equation:

-(125x^2-175x)


We get rid of parentheses

-125x^2-10x+175x-7=0

We add all the numbers together, and all the variables

-125x^2+165x-7=0

a = -125; b = 165; c = -7;
Δ = b2-4ac
Δ = 1652-4·(-125)·(-7)
Δ = 23725
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:

$\sqrt{\Delta}=\sqrt{23725}=\sqrt{25*949}=\sqrt{25}*\sqrt{949}=5\sqrt{949}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(165)-5\sqrt{949}}{2*-125}=\frac{-165-5\sqrt{949}}{-250}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(165)+5\sqrt{949}}{2*-125}=\frac{-165+5\sqrt{949}}{-250}
$