-61x=(8x+3)(x-1)

Solution for -61x=(8x+3)(x-1) equation:

-61x=(8x+3)(x-1)

We move all terms to the left:

-61x-((8x+3)(x-1))=0

We multiply parentheses ..

-((+8x^2-8x+3x-3))-61x=0


We calculate terms in parentheses: -((+8x^2-8x+3x-3)), so:

(+8x^2-8x+3x-3)

We get rid of parentheses

8x^2-8x+3x-3

We add all the numbers together, and all the variables

8x^2-5x-3

Back to the equation:

-(8x^2-5x-3)


We add all the numbers together, and all the variables

-61x-(8x^2-5x-3)=0

We get rid of parentheses

-8x^2-61x+5x+3=0

We add all the numbers together, and all the variables

-8x^2-56x+3=0

a = -8; b = -56; c = +3;
Δ = b2-4ac
Δ = -562-4·(-8)·3
Δ = 3232
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:

$\sqrt{\Delta}=\sqrt{3232}=\sqrt{16*202}=\sqrt{16}*\sqrt{202}=4\sqrt{202}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{202}}{2*-8}=\frac{56-4\sqrt{202}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{202}}{2*-8}=\frac{56+4\sqrt{202}}{-16}
$