10+x-3/1x=0

Solution for 10+x-3/1x=0 equation:

10+x-3/1x=0


Domain of the equation: 1x!=0

x∈R


We multiply all the terms by the denominator


x*1x+10*1x-3=0

Wy multiply elements

x^2+10x-3=0

a = 1; b = 10; c = -3;
Δ = b2-4ac
Δ = 102-4·1·(-3)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{7}}{2*1}=\frac{-10-4\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{7}}{2*1}=\frac{-10+4\sqrt{7}}{2}
$