(2x-3)-x(x-6)=-2(4x-7)

Solution for (2x-3)-x(x-6)=-2(4x-7) equation:

(2x-3)-x(x-6)=-2(4x-7)

We move all terms to the left:

(2x-3)-x(x-6)-(-2(4x-7))=0

We multiply parentheses

-x^2+(2x-3)+6x-(-2(4x-7))=0

We get rid of parentheses

-x^2+2x+6x-(-2(4x-7))-3=0


We calculate terms in parentheses: -(-2(4x-7)), so:

-2(4x-7)

We multiply parentheses

-8x+14

Back to the equation:

-(-8x+14)


We add all the numbers together, and all the variables

-1x^2+8x-(-8x+14)-3=0

We get rid of parentheses

-1x^2+8x+8x-14-3=0

We add all the numbers together, and all the variables

-1x^2+16x-17=0

a = -1; b = 16; c = -17;
Δ = b2-4ac
Δ = 162-4·(-1)·(-17)
Δ = 188
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{47}}{2*-1}=\frac{-16-2\sqrt{47}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{47}}{2*-1}=\frac{-16+2\sqrt{47}}{-2}
$