8/9x+5=7x-15

Solution for 8/9x+5=7x-15 equation:

8/9x+5=7x-15

We move all terms to the left:

8/9x+5-(7x-15)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

8/9x-7x+15+5=0

We multiply all the terms by the denominator


-7x*9x+15*9x+5*9x+8=0

Wy multiply elements

-63x^2+135x+45x+8=0

We add all the numbers together, and all the variables

-63x^2+180x+8=0

a = -63; b = 180; c = +8;
Δ = b2-4ac
Δ = 1802-4·(-63)·8
Δ = 34416
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:

$\sqrt{\Delta}=\sqrt{34416}=\sqrt{144*239}=\sqrt{144}*\sqrt{239}=12\sqrt{239}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-12\sqrt{239}}{2*-63}=\frac{-180-12\sqrt{239}}{-126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+12\sqrt{239}}{2*-63}=\frac{-180+12\sqrt{239}}{-126}
$