x2+x/2=10

Solution for x2+x/2=10 equation:

x2+x/2=10

We move all terms to the left:

x2+x/2-(10)=0

We add all the numbers together, and all the variables

x^2+x/2-10=0

We multiply all the terms by the denominator


x^2*2+x-10*2=0

We add all the numbers together, and all the variables

x^2*2+x-20=0

Wy multiply elements

2x^2+x-20=0

a = 2; b = 1; c = -20;
Δ = b2-4ac
Δ = 12-4·2·(-20)
Δ = 161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{161}}{2*2}=\frac{-1-\sqrt{161}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{161}}{2*2}=\frac{-1+\sqrt{161}}{4}
$