85=(11x+3)(5x-10)

Solution for 85=(11x+3)(5x-10) equation:

85=(11x+3)(5x-10)

We move all terms to the left:

85-((11x+3)(5x-10))=0

We multiply parentheses ..

-((+55x^2-110x+15x-30))+85=0


We calculate terms in parentheses: -((+55x^2-110x+15x-30)), so:

(+55x^2-110x+15x-30)

We get rid of parentheses

55x^2-110x+15x-30

We add all the numbers together, and all the variables

55x^2-95x-30

Back to the equation:

-(55x^2-95x-30)


We get rid of parentheses

-55x^2+95x+30+85=0

We add all the numbers together, and all the variables

-55x^2+95x+115=0

a = -55; b = 95; c = +115;
Δ = b2-4ac
Δ = 952-4·(-55)·115
Δ = 34325
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:

$\sqrt{\Delta}=\sqrt{34325}=\sqrt{25*1373}=\sqrt{25}*\sqrt{1373}=5\sqrt{1373}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(95)-5\sqrt{1373}}{2*-55}=\frac{-95-5\sqrt{1373}}{-110}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(95)+5\sqrt{1373}}{2*-55}=\frac{-95+5\sqrt{1373}}{-110}
$