7x-8x(-x+7)=-16+17x

Solution for 7x-8x(-x+7)=-16+17x equation:

7x-8x(-x+7)=-16+17x

We move all terms to the left:

7x-8x(-x+7)-(-16+17x)=0

We add all the numbers together, and all the variables

7x-8x(-1x+7)-(17x-16)=0

We multiply parentheses

8x^2+7x-56x-(17x-16)=0

We get rid of parentheses

8x^2+7x-56x-17x+16=0

We add all the numbers together, and all the variables

8x^2-66x+16=0

a = 8; b = -66; c = +16;
Δ = b2-4ac
Δ = -662-4·8·16
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-62}{2*8}=\frac{4}{16}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+62}{2*8}=\frac{128}{16}
=8
$