-1+3/2*x=4

Solution for -1+3/2*x=4 equation:

-1+3/2*x=4

We move all terms to the left:

-1+3/2*x-(4)=0


Domain of the equation: 2*x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/2*x-5=0

We multiply all the terms by the denominator


-5*2*x+3=0

Wy multiply elements

-10x*x+3=0

Wy multiply elements

-10x^2+3=0

a = -10; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-10)·3
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*-10}=\frac{0-2\sqrt{30}}{-20}
=-\frac{2\sqrt{30}}{-20}
=-\frac{\sqrt{30}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*-10}=\frac{0+2\sqrt{30}}{-20}
=\frac{2\sqrt{30}}{-20}
=\frac{\sqrt{30}}{-10}
$