10x=7x(x+6)

Solution for 10x=7x(x+6) equation:

10x=7x(x+6)

We move all terms to the left:

10x-(7x(x+6))=0


We calculate terms in parentheses: -(7x(x+6)), so:

7x(x+6)

We multiply parentheses

7x^2+42x

Back to the equation:

-(7x^2+42x)


We get rid of parentheses

-7x^2+10x-42x=0

We add all the numbers together, and all the variables

-7x^2-32x=0

a = -7; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-7)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-7}=\frac{0}{-14}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-7}=\frac{64}{-14}
=-4+4/7
$