(3x-5)2+5x=(x-8)(x+1)+20

Solution for (3x-5)2+5x=(x-8)(x+1)+20 equation:

(3x-5)2+5x=(x-8)(x+1)+20

We move all terms to the left:

(3x-5)2+5x-((x-8)(x+1)+20)=0

We add all the numbers together, and all the variables

5x+(3x-5)2-((x-8)(x+1)+20)=0

We multiply parentheses

5x+6x-((x-8)(x+1)+20)-10=0

We multiply parentheses ..

-((+x^2+x-8x-8)+20)+5x+6x-10=0


We calculate terms in parentheses: -((+x^2+x-8x-8)+20), so:

(+x^2+x-8x-8)+20

We get rid of parentheses

x^2+x-8x-8+20

We add all the numbers together, and all the variables

x^2-7x+12

Back to the equation:

-(x^2-7x+12)


We add all the numbers together, and all the variables

11x-(x^2-7x+12)-10=0

We get rid of parentheses

-x^2+11x+7x-12-10=0

We add all the numbers together, and all the variables

-1x^2+18x-22=0

a = -1; b = 18; c = -22;
Δ = b2-4ac
Δ = 182-4·(-1)·(-22)
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{59}}{2*-1}=\frac{-18-2\sqrt{59}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{59}}{2*-1}=\frac{-18+2\sqrt{59}}{-2}
$