3/4x+9=0.65x-12

Solution for 3/4x+9=0.65x-12 equation:

3/4x+9=0.65x-12

We move all terms to the left:

3/4x+9-(0.65x-12)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-0.65x+12+9=0

We multiply all the terms by the denominator


-(0.65x)*4x+12*4x+9*4x+3=0

We add all the numbers together, and all the variables

-(+0.65x)*4x+12*4x+9*4x+3=0

We multiply parentheses

-0x^2+12*4x+9*4x+3=0

Wy multiply elements

-0x^2+48x+36x+3=0

We add all the numbers together, and all the variables

-1x^2+84x+3=0

a = -1; b = 84; c = +3;
Δ = b2-4ac
Δ = 842-4·(-1)·3
Δ = 7068
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:

$\sqrt{\Delta}=\sqrt{7068}=\sqrt{4*1767}=\sqrt{4}*\sqrt{1767}=2\sqrt{1767}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-2\sqrt{1767}}{2*-1}=\frac{-84-2\sqrt{1767}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+2\sqrt{1767}}{2*-1}=\frac{-84+2\sqrt{1767}}{-2}
$