4x(x-7)=7/8

Solution for 4x(x-7)=7/8 equation:

4x(x-7)=7/8

We move all terms to the left:

4x(x-7)-(7/8)=0

We add all the numbers together, and all the variables

4x(x-7)-(+7/8)=0

We multiply parentheses

4x^2-28x-(+7/8)=0

We get rid of parentheses

4x^2-28x-7/8=0

We multiply all the terms by the denominator


4x^2*8-28x*8-7=0

Wy multiply elements

32x^2-224x-7=0

a = 32; b = -224; c = -7;
Δ = b2-4ac
Δ = -2242-4·32·(-7)
Δ = 51072
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:

$\sqrt{\Delta}=\sqrt{51072}=\sqrt{64*798}=\sqrt{64}*\sqrt{798}=8\sqrt{798}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-224)-8\sqrt{798}}{2*32}=\frac{224-8\sqrt{798}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-224)+8\sqrt{798}}{2*32}=\frac{224+8\sqrt{798}}{64}
$