19x-4+12x=16x-1+14/0,33x

Solution for 19x-4+12x=16x-1+14/0,33x equation:

19x-4+12x=16x-1+14/0.33x

We move all terms to the left:

19x-4+12x-(16x-1+14/0.33x)=0


Domain of the equation: 0.33x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

19x+12x-(16x+14/0.33x-1)-4=0

We add all the numbers together, and all the variables

31x-(16x+14/0.33x-1)-4=0

We get rid of parentheses

31x-16x-14/0.33x+1-4=0

We multiply all the terms by the denominator


31x*0.33x-16x*0.33x+1*0.33x-4*0.33x-14=0

Wy multiply elements

0x^2+0x^2+0x+0x-14=0

We add all the numbers together, and all the variables

2x^2+2x-14=0

a = 2; b = 2; c = -14;
Δ = b2-4ac
Δ = 22-4·2·(-14)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{29}}{2*2}=\frac{-2-2\sqrt{29}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{29}}{2*2}=\frac{-2+2\sqrt{29}}{4}
$