x-3/4x-0.18x=313.5

Solution for x-3/4x-0.18x=313.5 equation:

x-3/4x-0.18x=313.5

We move all terms to the left:

x-3/4x-0.18x-(313.5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

0.82x-3/4x-313.5=0

We multiply all the terms by the denominator


(0.82x)*4x-(313.5)*4x-3=0

We add all the numbers together, and all the variables

(+0.82x)*4x-(313.5)*4x-3=0

We multiply parentheses

0x^2-1254x-3=0

We add all the numbers together, and all the variables

x^2-1254x-3=0

a = 1; b = -1254; c = -3;
Δ = b2-4ac
Δ = -12542-4·1·(-3)
Δ = 1572528
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:

$\sqrt{\Delta}=\sqrt{1572528}=\sqrt{524176*3}=\sqrt{524176}*\sqrt{3}=724\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1254)-724\sqrt{3}}{2*1}=\frac{1254-724\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1254)+724\sqrt{3}}{2*1}=\frac{1254+724\sqrt{3}}{2}
$