7/4x+15=9x-14

Solution for 7/4x+15=9x-14 equation:

7/4x+15=9x-14

We move all terms to the left:

7/4x+15-(9x-14)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

7/4x-9x+14+15=0

We multiply all the terms by the denominator


-9x*4x+14*4x+15*4x+7=0

Wy multiply elements

-36x^2+56x+60x+7=0

We add all the numbers together, and all the variables

-36x^2+116x+7=0

a = -36; b = 116; c = +7;
Δ = b2-4ac
Δ = 1162-4·(-36)·7
Δ = 14464
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:

$\sqrt{\Delta}=\sqrt{14464}=\sqrt{64*226}=\sqrt{64}*\sqrt{226}=8\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(116)-8\sqrt{226}}{2*-36}=\frac{-116-8\sqrt{226}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(116)+8\sqrt{226}}{2*-36}=\frac{-116+8\sqrt{226}}{-72}
$