7x-4=3/16x+5

Solution for 7x-4=3/16x+5 equation:

7x-4=3/16x+5

We move all terms to the left:

7x-4-(3/16x+5)=0


Domain of the equation: 16x+5)!=0

x∈R


We get rid of parentheses

7x-3/16x-5-4=0

We multiply all the terms by the denominator


7x*16x-5*16x-4*16x-3=0

Wy multiply elements

112x^2-80x-64x-3=0

We add all the numbers together, and all the variables

112x^2-144x-3=0

a = 112; b = -144; c = -3;
Δ = b2-4ac
Δ = -1442-4·112·(-3)
Δ = 22080
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:

$\sqrt{\Delta}=\sqrt{22080}=\sqrt{64*345}=\sqrt{64}*\sqrt{345}=8\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-8\sqrt{345}}{2*112}=\frac{144-8\sqrt{345}}{224}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+8\sqrt{345}}{2*112}=\frac{144+8\sqrt{345}}{224}
$