6x-2x(x-1)=5x-7

Solution for 6x-2x(x-1)=5x-7 equation:

6x-2x(x-1)=5x-7

We move all terms to the left:

6x-2x(x-1)-(5x-7)=0

We multiply parentheses

-2x^2+6x+2x-(5x-7)=0

We get rid of parentheses

-2x^2+6x+2x-5x+7=0

We add all the numbers together, and all the variables

-2x^2+3x+7=0

a = -2; b = 3; c = +7;
Δ = b2-4ac
Δ = 32-4·(-2)·7
Δ = 65
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{-(3)-\sqrt{65}}{2*-2}=\frac{-3-\sqrt{65}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{65}}{2*-2}=\frac{-3+\sqrt{65}}{-4}
$