145+1/4x=1.5x

Solution for 145+1/4x=1.5x equation:

145+1/4x=1.5x

We move all terms to the left:

145+1/4x-(1.5x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(+1.5x)+145=0

We get rid of parentheses

1/4x-1.5x+145=0

We multiply all the terms by the denominator


-(1.5x)*4x+145*4x+1=0

We add all the numbers together, and all the variables

-(+1.5x)*4x+145*4x+1=0

We multiply parentheses

-4x^2+145*4x+1=0

Wy multiply elements

-4x^2+580x+1=0

a = -4; b = 580; c = +1;
Δ = b2-4ac
Δ = 5802-4·(-4)·1
Δ = 336416
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:

$\sqrt{\Delta}=\sqrt{336416}=\sqrt{16*21026}=\sqrt{16}*\sqrt{21026}=4\sqrt{21026}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(580)-4\sqrt{21026}}{2*-4}=\frac{-580-4\sqrt{21026}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(580)+4\sqrt{21026}}{2*-4}=\frac{-580+4\sqrt{21026}}{-8}
$