x+x(8/5)=78

Solution for x+x(8/5)=78 equation:

x+x(8/5)=78

We move all terms to the left:

x+x(8/5)-(78)=0

We add all the numbers together, and all the variables

x+x(+8/5)-78=0

We multiply parentheses

8x^2+x-78=0

a = 8; b = 1; c = -78;
Δ = b2-4ac
Δ = 12-4·8·(-78)
Δ = 2497
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{2497}}{2*8}=\frac{-1-\sqrt{2497}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2497}}{2*8}=\frac{-1+\sqrt{2497}}{16}
$