3x=11/4x+7

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Solution for 3x=11/4x+7 equation: 



3x=11/4x+7

We move all terms to the left:

3x-(11/4x+7)=0



Domain of the equation: 4x+7)!=0

x∈R



We get rid of parentheses

3x-11/4x-7=0

We multiply all the terms by the denominator


3x*4x-7*4x-11=0

Wy multiply elements

12x^2-28x-11=0

a = 12; b = -28; c = -11;
Δ = b2-4ac
Δ = -282-4·12·(-11)
Δ = 1312
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:


$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{82}}{2*12}=\frac{28-4\sqrt{82}}{24}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{82}}{2*12}=\frac{28+4\sqrt{82}}{24}
$

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