z^2+10z+25=2z^2+3z+7

Solution for z^2+10z+25=2z^2+3z+7 equation:

z^2+10z+25=2z^2+3z+7

We move all terms to the left:

z^2+10z+25-(2z^2+3z+7)=0

We get rid of parentheses

z^2-2z^2+10z-3z-7+25=0

We add all the numbers together, and all the variables

-1z^2+7z+18=0

a = -1; b = 7; c = +18;
Δ = b2-4ac
Δ = 72-4·(-1)·18
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*-1}=\frac{-18}{-2}
=+9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*-1}=\frac{4}{-2}
=-2
$