85x=(85-x)(x+17)

Solution for 85x=(85-x)(x+17) equation:

85x=(85-x)(x+17)

We move all terms to the left:

85x-((85-x)(x+17))=0

We add all the numbers together, and all the variables

85x-((-1x+85)(x+17))=0

We multiply parentheses ..

-((-1x^2-17x+85x+1445))+85x=0


We calculate terms in parentheses: -((-1x^2-17x+85x+1445)), so:

(-1x^2-17x+85x+1445)

We get rid of parentheses

-1x^2-17x+85x+1445

We add all the numbers together, and all the variables

-1x^2+68x+1445

Back to the equation:

-(-1x^2+68x+1445)


We get rid of parentheses

1x^2-68x+85x-1445=0

We add all the numbers together, and all the variables

x^2+17x-1445=0

a = 1; b = 17; c = -1445;
Δ = b2-4ac
Δ = 172-4·1·(-1445)
Δ = 6069
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:

$\sqrt{\Delta}=\sqrt{6069}=\sqrt{289*21}=\sqrt{289}*\sqrt{21}=17\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17\sqrt{21}}{2*1}=\frac{-17-17\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17\sqrt{21}}{2*1}=\frac{-17+17\sqrt{21}}{2}
$