-7(8/7)x-3/4=20(-8/7)

Solution for -7(8/7)x-3/4=20(-8/7) equation:

-7(8/7)x-3/4=20(-8/7)

We move all terms to the left:

-7(8/7)x-3/4-(20(-8/7))=0


Domain of the equation: 7)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-7(+8/7)x-3/4-(20(-8/7))=0

We multiply parentheses

-56x^2-3/4-(20(-8/7))=0

We calculate fractions


-56x^2+()/()+()/()=0

We add all the numbers together, and all the variables

-56x^2+2=0

a = -56; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-56)·2
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{7}}{2*-56}=\frac{0-8\sqrt{7}}{-112}
=-\frac{8\sqrt{7}}{-112}
=-\frac{\sqrt{7}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{7}}{2*-56}=\frac{0+8\sqrt{7}}{-112}
=\frac{8\sqrt{7}}{-112}
=\frac{\sqrt{7}}{-14}
$