2(8x-1)(x+5)=59

Solution for 2(8x-1)(x+5)=59 equation:

2(8x-1)(x+5)=59

We move all terms to the left:

2(8x-1)(x+5)-(59)=0

We multiply parentheses ..

2(+8x^2+40x-1x-5)-59=0

We multiply parentheses

16x^2+80x-2x-10-59=0

We add all the numbers together, and all the variables

16x^2+78x-69=0

a = 16; b = 78; c = -69;
Δ = b2-4ac
Δ = 782-4·16·(-69)
Δ = 10500
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:

$\sqrt{\Delta}=\sqrt{10500}=\sqrt{100*105}=\sqrt{100}*\sqrt{105}=10\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-10\sqrt{105}}{2*16}=\frac{-78-10\sqrt{105}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+10\sqrt{105}}{2*16}=\frac{-78+10\sqrt{105}}{32}
$