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x+7/8x=960

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Solution for x+7/8x=960 equation:



x+7/8x=960
We move all terms to the left:
x+7/8x-(960)=0
Domain of the equation: 8x!=0
x!=0/8
x!=0
x∈R
We multiply all the terms by the denominator
x*8x-960*8x+7=0
Wy multiply elements
8x^2-7680x+7=0
a = 8; b = -7680; c = +7;
Δ = b2-4ac
Δ = -76802-4·8·7
Δ = 58982176
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{58982176}=\sqrt{1936*30466}=\sqrt{1936}*\sqrt{30466}=44\sqrt{30466}
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7680)-44\sqrt{30466}}{2*8}=\frac{7680-44\sqrt{30466}}{16}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7680)+44\sqrt{30466}}{2*8}=\frac{7680+44\sqrt{30466}}{16}

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