X=85/4x-3

Solution for X=85/4x-3 equation:

X=85/4X-3

We move all terms to the left:

X-(85/4X-3)=0


Domain of the equation: 4X-3)!=0

X∈R


We get rid of parentheses

X-85/4X+3=0

We multiply all the terms by the denominator


X*4X+3*4X-85=0

Wy multiply elements

4X^2+12X-85=0

a = 4; b = 12; c = -85;
Δ = b2-4ac
Δ = 122-4·4·(-85)
Δ = 1504
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:

$\sqrt{\Delta}=\sqrt{1504}=\sqrt{16*94}=\sqrt{16}*\sqrt{94}=4\sqrt{94}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{94}}{2*4}=\frac{-12-4\sqrt{94}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{94}}{2*4}=\frac{-12+4\sqrt{94}}{8}
$