(8x-13)=(5x+17)(x+21)

Solution for (8x-13)=(5x+17)(x+21) equation:

(8x-13)=(5x+17)(x+21)

We move all terms to the left:

(8x-13)-((5x+17)(x+21))=0

We get rid of parentheses

8x-((5x+17)(x+21))-13=0

We multiply parentheses ..

-((+5x^2+105x+17x+357))+8x-13=0


We calculate terms in parentheses: -((+5x^2+105x+17x+357)), so:

(+5x^2+105x+17x+357)

We get rid of parentheses

5x^2+105x+17x+357

We add all the numbers together, and all the variables

5x^2+122x+357

Back to the equation:

-(5x^2+122x+357)


We add all the numbers together, and all the variables

8x-(5x^2+122x+357)-13=0

We get rid of parentheses

-5x^2+8x-122x-357-13=0

We add all the numbers together, and all the variables

-5x^2-114x-370=0

a = -5; b = -114; c = -370;
Δ = b2-4ac
Δ = -1142-4·(-5)·(-370)
Δ = 5596
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:

$\sqrt{\Delta}=\sqrt{5596}=\sqrt{4*1399}=\sqrt{4}*\sqrt{1399}=2\sqrt{1399}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-2\sqrt{1399}}{2*-5}=\frac{114-2\sqrt{1399}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+2\sqrt{1399}}{2*-5}=\frac{114+2\sqrt{1399}}{-10}
$