2x+3/4x=297

Solution for 2x+3/4x=297 equation:

2x+3/4x=297

We move all terms to the left:

2x+3/4x-(297)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


2x*4x-297*4x+3=0

Wy multiply elements

8x^2-1188x+3=0

a = 8; b = -1188; c = +3;
Δ = b2-4ac
Δ = -11882-4·8·3
Δ = 1411248
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:

$\sqrt{\Delta}=\sqrt{1411248}=\sqrt{16*88203}=\sqrt{16}*\sqrt{88203}=4\sqrt{88203}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1188)-4\sqrt{88203}}{2*8}=\frac{1188-4\sqrt{88203}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1188)+4\sqrt{88203}}{2*8}=\frac{1188+4\sqrt{88203}}{16}
$