X=5/4x-10

Solution for X=5/4x-10 equation:

X=5/4X-10

We move all terms to the left:

X-(5/4X-10)=0


Domain of the equation: 4X-10)!=0

X∈R


We get rid of parentheses

X-5/4X+10=0

We multiply all the terms by the denominator


X*4X+10*4X-5=0

Wy multiply elements

4X^2+40X-5=0

a = 4; b = 40; c = -5;
Δ = b2-4ac
Δ = 402-4·4·(-5)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{105}}{2*4}=\frac{-40-4\sqrt{105}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{105}}{2*4}=\frac{-40+4\sqrt{105}}{8}
$