8x=2(-13/16)+3

Solution for 8x=2(-13/16)+3 equation:

8x=2(-13/16)+3

We move all terms to the left:

8x-(2(-13/16)+3)=0

We multiply all the terms by the denominator


8x*16)+3)-(2(-13=0

Wy multiply elements

128x^2-13=0

a = 128; b = 0; c = -13;
Δ = b2-4ac
Δ = 02-4·128·(-13)
Δ = 6656
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:

$\sqrt{\Delta}=\sqrt{6656}=\sqrt{256*26}=\sqrt{256}*\sqrt{26}=16\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{26}}{2*128}=\frac{0-16\sqrt{26}}{256}
=-\frac{16\sqrt{26}}{256}
=-\frac{\sqrt{26}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{26}}{2*128}=\frac{0+16\sqrt{26}}{256}
=\frac{16\sqrt{26}}{256}
=\frac{\sqrt{26}}{16}
$