(8x+7)(4x-1)=78

Solution for (8x+7)(4x-1)=78 equation:

(8x+7)(4x-1)=78

We move all terms to the left:

(8x+7)(4x-1)-(78)=0

We multiply parentheses ..

(+32x^2-8x+28x-7)-78=0

We get rid of parentheses

32x^2-8x+28x-7-78=0

We add all the numbers together, and all the variables

32x^2+20x-85=0

a = 32; b = 20; c = -85;
Δ = b2-4ac
Δ = 202-4·32·(-85)
Δ = 11280
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:

$\sqrt{\Delta}=\sqrt{11280}=\sqrt{16*705}=\sqrt{16}*\sqrt{705}=4\sqrt{705}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{705}}{2*32}=\frac{-20-4\sqrt{705}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{705}}{2*32}=\frac{-20+4\sqrt{705}}{64}
$