9x-4=-9/15x+12

Solution for 9x-4=-9/15x+12 equation:

9x-4=-9/15x+12

We move all terms to the left:

9x-4-(-9/15x+12)=0


Domain of the equation: 15x+12)!=0

x∈R


We get rid of parentheses

9x+9/15x-12-4=0

We multiply all the terms by the denominator


9x*15x-12*15x-4*15x+9=0

Wy multiply elements

135x^2-180x-60x+9=0

We add all the numbers together, and all the variables

135x^2-240x+9=0

a = 135; b = -240; c = +9;
Δ = b2-4ac
Δ = -2402-4·135·9
Δ = 52740
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:

$\sqrt{\Delta}=\sqrt{52740}=\sqrt{36*1465}=\sqrt{36}*\sqrt{1465}=6\sqrt{1465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-6\sqrt{1465}}{2*135}=\frac{240-6\sqrt{1465}}{270}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+6\sqrt{1465}}{2*135}=\frac{240+6\sqrt{1465}}{270}
$