-9x(7x-10)=x

Solution for -9x(7x-10)=x equation:

-9x(7x-10)=x

We move all terms to the left:

-9x(7x-10)-(x)=0

We add all the numbers together, and all the variables

-1x-9x(7x-10)=0

We multiply parentheses

-63x^2-1x+90x=0

We add all the numbers together, and all the variables

-63x^2+89x=0

a = -63; b = 89; c = 0;
Δ = b2-4ac
Δ = 892-4·(-63)·0
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(89)-89}{2*-63}=\frac{-178}{-126}
=1+26/63
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(89)+89}{2*-63}=\frac{0}{-126}
=0
$