8x=(7x+6)5x

Solution for 8x=(7x+6)5x equation:

8x=(7x+6)5x

We move all terms to the left:

8x-((7x+6)5x)=0


We calculate terms in parentheses: -((7x+6)5x), so:

(7x+6)5x

We multiply parentheses

35x^2+30x

Back to the equation:

-(35x^2+30x)


We get rid of parentheses

-35x^2+8x-30x=0

We add all the numbers together, and all the variables

-35x^2-22x=0

a = -35; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-35)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*-35}=\frac{0}{-70}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*-35}=\frac{44}{-70}
=-22/35
$