2x(8x-25)=9x+34

Solution for 2x(8x-25)=9x+34 equation:

2x(8x-25)=9x+34

We move all terms to the left:

2x(8x-25)-(9x+34)=0

We multiply parentheses

16x^2-50x-(9x+34)=0

We get rid of parentheses

16x^2-50x-9x-34=0

We add all the numbers together, and all the variables

16x^2-59x-34=0

a = 16; b = -59; c = -34;
Δ = b2-4ac
Δ = -592-4·16·(-34)
Δ = 5657
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{-(-59)-\sqrt{5657}}{2*16}=\frac{59-\sqrt{5657}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{5657}}{2*16}=\frac{59+\sqrt{5657}}{32}
$