3/4x+1.2x=15

Solution for 3/4x+1.2x=15 equation:

3/4x+1.2x=15

We move all terms to the left:

3/4x+1.2x-(15)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1.2x+3/4x-15=0

We multiply all the terms by the denominator


(1.2x)*4x-15*4x+3=0

We add all the numbers together, and all the variables

(+1.2x)*4x-15*4x+3=0

We multiply parentheses

4x^2-15*4x+3=0

Wy multiply elements

4x^2-60x+3=0

a = 4; b = -60; c = +3;
Δ = b2-4ac
Δ = -602-4·4·3
Δ = 3552
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:

$\sqrt{\Delta}=\sqrt{3552}=\sqrt{16*222}=\sqrt{16}*\sqrt{222}=4\sqrt{222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{222}}{2*4}=\frac{60-4\sqrt{222}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{222}}{2*4}=\frac{60+4\sqrt{222}}{8}
$