8x(2x-5)-6(3x-7)=1

Solution for 8x(2x-5)-6(3x-7)=1 equation:

8x(2x-5)-6(3x-7)=1

We move all terms to the left:

8x(2x-5)-6(3x-7)-(1)=0

We multiply parentheses

16x^2-40x-18x+42-1=0

We add all the numbers together, and all the variables

16x^2-58x+41=0

a = 16; b = -58; c = +41;
Δ = b2-4ac
Δ = -582-4·16·41
Δ = 740
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:

$\sqrt{\Delta}=\sqrt{740}=\sqrt{4*185}=\sqrt{4}*\sqrt{185}=2\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-2\sqrt{185}}{2*16}=\frac{58-2\sqrt{185}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+2\sqrt{185}}{2*16}=\frac{58+2\sqrt{185}}{32}
$