7x^2-14x+5=-x^2

Solution for 7x^2-14x+5=-x^2 equation:

7x^2-14x+5=-x^2

We move all terms to the left:

7x^2-14x+5-(-x^2)=0

We get rid of parentheses

7x^2+x^2-14x+5=0

We add all the numbers together, and all the variables

8x^2-14x+5=0

a = 8; b = -14; c = +5;
Δ = b2-4ac
Δ = -142-4·8·5
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6}{2*8}=\frac{8}{16}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6}{2*8}=\frac{20}{16}
=1+1/4
$