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4x+9/7x-8=0
Domain of the equation: 7x!=0We multiply all the terms by the denominator
x!=0/7
x!=0
x∈R
4x*7x-8*7x+9=0
Wy multiply elements
28x^2-56x+9=0
a = 28; b = -56; c = +9;
Δ = b2-4ac
Δ = -562-4·28·9
Δ = 2128
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2128}=\sqrt{16*133}=\sqrt{16}*\sqrt{133}=4\sqrt{133}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{133}}{2*28}=\frac{56-4\sqrt{133}}{56} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{133}}{2*28}=\frac{56+4\sqrt{133}}{56} $
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