(x-1)(16x+17)=(4x-5)2

Solution for (x-1)(16x+17)=(4x-5)2 equation:

(x-1)(16x+17)=(4x-5)2

We move all terms to the left:

(x-1)(16x+17)-((4x-5)2)=0

We multiply parentheses ..

(+16x^2+17x-16x-17)-((4x-5)2)=0


We calculate terms in parentheses: -((4x-5)2), so:

(4x-5)2

We multiply parentheses

8x-10

Back to the equation:

-(8x-10)


We get rid of parentheses

16x^2+17x-16x-8x-17+10=0

We add all the numbers together, and all the variables

16x^2-7x-7=0

a = 16; b = -7; c = -7;
Δ = b2-4ac
Δ = -72-4·16·(-7)
Δ = 497
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{497}}{2*16}=\frac{7-\sqrt{497}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{497}}{2*16}=\frac{7+\sqrt{497}}{32}
$