2x+774=15/8x-4

Solution for 2x+774=15/8x-4 equation:

2x+774=15/8x-4

We move all terms to the left:

2x+774-(15/8x-4)=0


Domain of the equation: 8x-4)!=0

x∈R


We get rid of parentheses

2x-15/8x+4+774=0

We multiply all the terms by the denominator


2x*8x+4*8x+774*8x-15=0

Wy multiply elements

16x^2+32x+6192x-15=0

We add all the numbers together, and all the variables

16x^2+6224x-15=0

a = 16; b = 6224; c = -15;
Δ = b2-4ac
Δ = 62242-4·16·(-15)
Δ = 38739136
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:

$\sqrt{\Delta}=\sqrt{38739136}=\sqrt{64*605299}=\sqrt{64}*\sqrt{605299}=8\sqrt{605299}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6224)-8\sqrt{605299}}{2*16}=\frac{-6224-8\sqrt{605299}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6224)+8\sqrt{605299}}{2*16}=\frac{-6224+8\sqrt{605299}}{32}
$