-5x2+5x+10=10/11

Solution for -5x2+5x+10=10/11 equation:

-5x^2+5x+10=10/11

We move all terms to the left:

-5x^2+5x+10-(10/11)=0

We add all the numbers together, and all the variables

-5x^2+5x+10-(+10/11)=0

We get rid of parentheses

-5x^2+5x+10-10/11=0

We multiply all the terms by the denominator


-5x^2*11+5x*11-10+10*11=0

We add all the numbers together, and all the variables

-5x^2*11+5x*11+100=0

Wy multiply elements

-55x^2+55x+100=0

a = -55; b = 55; c = +100;
Δ = b2-4ac
Δ = 552-4·(-55)·100
Δ = 25025
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:

$\sqrt{\Delta}=\sqrt{25025}=\sqrt{25*1001}=\sqrt{25}*\sqrt{1001}=5\sqrt{1001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-5\sqrt{1001}}{2*-55}=\frac{-55-5\sqrt{1001}}{-110}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+5\sqrt{1001}}{2*-55}=\frac{-55+5\sqrt{1001}}{-110}
$