2x+3/4*2x-28=0

Solution for 2x+3/4*2x-28=0 equation:

2x+3/4*2x-28=0


Domain of the equation: 4*2x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


2x*4*2x-28*4*2x+3=0

Wy multiply elements

16x^2*2-224x*2+3=0

Wy multiply elements

32x^2-448x+3=0

a = 32; b = -448; c = +3;
Δ = b2-4ac
Δ = -4482-4·32·3
Δ = 200320
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:

$\sqrt{\Delta}=\sqrt{200320}=\sqrt{64*3130}=\sqrt{64}*\sqrt{3130}=8\sqrt{3130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-448)-8\sqrt{3130}}{2*32}=\frac{448-8\sqrt{3130}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-448)+8\sqrt{3130}}{2*32}=\frac{448+8\sqrt{3130}}{64}
$