17x(5x+3)=401+35x

Solution for 17x(5x+3)=401+35x equation:

17x(5x+3)=401+35x

We move all terms to the left:

17x(5x+3)-(401+35x)=0

We add all the numbers together, and all the variables

17x(5x+3)-(35x+401)=0

We multiply parentheses

85x^2+51x-(35x+401)=0

We get rid of parentheses

85x^2+51x-35x-401=0

We add all the numbers together, and all the variables

85x^2+16x-401=0

a = 85; b = 16; c = -401;
Δ = b2-4ac
Δ = 162-4·85·(-401)
Δ = 136596
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:

$\sqrt{\Delta}=\sqrt{136596}=\sqrt{4*34149}=\sqrt{4}*\sqrt{34149}=2\sqrt{34149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{34149}}{2*85}=\frac{-16-2\sqrt{34149}}{170}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{34149}}{2*85}=\frac{-16+2\sqrt{34149}}{170}
$