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4x-3/4x+10=0
Domain of the equation: 4x!=0We multiply all the terms by the denominator
x!=0/4
x!=0
x∈R
4x*4x+10*4x-3=0
Wy multiply elements
16x^2+40x-3=0
a = 16; b = 40; c = -3;
Δ = b2-4ac
Δ = 402-4·16·(-3)
Δ = 1792
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-16\sqrt{7}}{2*16}=\frac{-40-16\sqrt{7}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+16\sqrt{7}}{2*16}=\frac{-40+16\sqrt{7}}{32} $
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