23x+1=7/16x+3

Solution for 23x+1=7/16x+3 equation:

23x+1=7/16x+3

We move all terms to the left:

23x+1-(7/16x+3)=0


Domain of the equation: 16x+3)!=0

x∈R


We get rid of parentheses

23x-7/16x-3+1=0

We multiply all the terms by the denominator


23x*16x-3*16x+1*16x-7=0

Wy multiply elements

368x^2-48x+16x-7=0

We add all the numbers together, and all the variables

368x^2-32x-7=0

a = 368; b = -32; c = -7;
Δ = b2-4ac
Δ = -322-4·368·(-7)
Δ = 11328
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:

$\sqrt{\Delta}=\sqrt{11328}=\sqrt{64*177}=\sqrt{64}*\sqrt{177}=8\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{177}}{2*368}=\frac{32-8\sqrt{177}}{736}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{177}}{2*368}=\frac{32+8\sqrt{177}}{736}
$