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7/4x+15=9x-14
We move all terms to the left:
7/4x+15-(9x-14)=0
Domain of the equation: 4x!=0We get rid of parentheses
x!=0/4
x!=0
x∈R
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} $
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