X^2+6x+11/10=0

Solution for X^2+6x+11/10=0 equation:

X^2+6X+11/10=0

We multiply all the terms by the denominator


X^2*10+6X*10+11=0

Wy multiply elements

10X^2+60X+11=0

a = 10; b = 60; c = +11;
Δ = b2-4ac
Δ = 602-4·10·11
Δ = 3160
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:

$\sqrt{\Delta}=\sqrt{3160}=\sqrt{4*790}=\sqrt{4}*\sqrt{790}=2\sqrt{790}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{790}}{2*10}=\frac{-60-2\sqrt{790}}{20}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{790}}{2*10}=\frac{-60+2\sqrt{790}}{20}
$