(6x-10)(7x+8)=x

Solution for (6x-10)(7x+8)=x equation:

(6x-10)(7x+8)=x

We move all terms to the left:

(6x-10)(7x+8)-(x)=0

We add all the numbers together, and all the variables

-1x+(6x-10)(7x+8)=0

We multiply parentheses ..

(+42x^2+48x-70x-80)-1x=0

We get rid of parentheses

42x^2+48x-70x-1x-80=0

We add all the numbers together, and all the variables

42x^2-23x-80=0

a = 42; b = -23; c = -80;
Δ = b2-4ac
Δ = -232-4·42·(-80)
Δ = 13969
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{-(-23)-\sqrt{13969}}{2*42}=\frac{23-\sqrt{13969}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{13969}}{2*42}=\frac{23+\sqrt{13969}}{84}
$