5x+4=3/8x+12

Solution for 5x+4=3/8x+12 equation:

5x+4=3/8x+12

We move all terms to the left:

5x+4-(3/8x+12)=0


Domain of the equation: 8x+12)!=0

x∈R


We get rid of parentheses

5x-3/8x-12+4=0

We multiply all the terms by the denominator


5x*8x-12*8x+4*8x-3=0

Wy multiply elements

40x^2-96x+32x-3=0

We add all the numbers together, and all the variables

40x^2-64x-3=0

a = 40; b = -64; c = -3;
Δ = b2-4ac
Δ = -642-4·40·(-3)
Δ = 4576
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:

$\sqrt{\Delta}=\sqrt{4576}=\sqrt{16*286}=\sqrt{16}*\sqrt{286}=4\sqrt{286}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{286}}{2*40}=\frac{64-4\sqrt{286}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{286}}{2*40}=\frac{64+4\sqrt{286}}{80}
$