7z^2+z+1=2z^2-9z+7

Solution for 7z^2+z+1=2z^2-9z+7 equation:

7z^2+z+1=2z^2-9z+7

We move all terms to the left:

7z^2+z+1-(2z^2-9z+7)=0

We get rid of parentheses

7z^2-2z^2+z+9z-7+1=0

We add all the numbers together, and all the variables

5z^2+10z-6=0

a = 5; b = 10; c = -6;
Δ = b2-4ac
Δ = 102-4·5·(-6)
Δ = 220
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{55}}{2*5}=\frac{-10-2\sqrt{55}}{10}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{55}}{2*5}=\frac{-10+2\sqrt{55}}{10}
$