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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+32x^2-8x+28x-7)), so:

(+32x^2-8x+28x-7)

We get rid of parentheses

32x^2-8x+28x-7

We add all the numbers together, and all the variables

32x^2+20x-7

Back to the equation:

-(32x^2+20x-7)


We get rid of parentheses

-32x^2-20x+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}
$