5x2-10x2=-7+x+x2

Solution for 5x2-10x2=-7+x+x2 equation:

5x^2-10x^2=-7+x+x2

We move all terms to the left:

5x^2-10x^2-(-7+x+x2)=0

We add all the numbers together, and all the variables

5x^2-10x^2-(+x+x^2-7)=0

We add all the numbers together, and all the variables

-5x^2-(+x+x^2-7)=0

We get rid of parentheses

-5x^2-x^2-x+7=0

We add all the numbers together, and all the variables

-6x^2-1x+7=0

a = -6; b = -1; c = +7;
Δ = b2-4ac
Δ = -12-4·(-6)·7
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-13}{2*-6}=\frac{-12}{-12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+13}{2*-6}=\frac{14}{-12}
=-1+1/6
$