8z-10=z2-7z+3

Solution for 8z-10=z2-7z+3 equation:

8z-10=z2-7z+3

We move all terms to the left:

8z-10-(z2-7z+3)=0

We add all the numbers together, and all the variables

-(+z^2-7z+3)+8z-10=0

We get rid of parentheses

-z^2+7z+8z-3-10=0

We add all the numbers together, and all the variables

-1z^2+15z-13=0

a = -1; b = 15; c = -13;
Δ = b2-4ac
Δ = 152-4·(-1)·(-13)
Δ = 173
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{173}}{2*-1}=\frac{-15-\sqrt{173}}{-2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{173}}{2*-1}=\frac{-15+\sqrt{173}}{-2}
$