(3/4)x=61.5

Solution for (3/4)x=61.5 equation:

(3/4)x=61.5

We move all terms to the left:

(3/4)x-(61.5)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/4)x-(61.5)=0

We add all the numbers together, and all the variables

(+3/4)x-61.5=0

We multiply parentheses

3x^2-61.5=0

a = 3; b = 0; c = -61.5;
Δ = b2-4ac
Δ = 02-4·3·(-61.5)
Δ = 738
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:

$\sqrt{\Delta}=\sqrt{738}=\sqrt{9*82}=\sqrt{9}*\sqrt{82}=3\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{82}}{2*3}=\frac{0-3\sqrt{82}}{6}
=-\frac{3\sqrt{82}}{6}
=-\frac{\sqrt{82}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{82}}{2*3}=\frac{0+3\sqrt{82}}{6}
=\frac{3\sqrt{82}}{6}
=\frac{\sqrt{82}}{2}
$