3/4x+7=22x=

Solution for 3/4x+7=22x= equation:

3/4x+7=22x=

We move all terms to the left:

3/4x+7-(22x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-22x+3/4x+7=0

We multiply all the terms by the denominator


-22x*4x+7*4x+3=0

Wy multiply elements

-88x^2+28x+3=0

a = -88; b = 28; c = +3;
Δ = b2-4ac
Δ = 282-4·(-88)·3
Δ = 1840
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:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{115}}{2*-88}=\frac{-28-4\sqrt{115}}{-176}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{115}}{2*-88}=\frac{-28+4\sqrt{115}}{-176}
$