2x(x+3x-5)=78

Solution for 2x(x+3x-5)=78 equation:

2x(x+3x-5)=78

We move all terms to the left:

2x(x+3x-5)-(78)=0

We add all the numbers together, and all the variables

2x(4x-5)-78=0

We multiply parentheses

8x^2-10x-78=0

a = 8; b = -10; c = -78;
Δ = b2-4ac
Δ = -102-4·8·(-78)
Δ = 2596
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:

$\sqrt{\Delta}=\sqrt{2596}=\sqrt{4*649}=\sqrt{4}*\sqrt{649}=2\sqrt{649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{649}}{2*8}=\frac{10-2\sqrt{649}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{649}}{2*8}=\frac{10+2\sqrt{649}}{16}
$