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

Solution for 8z^2-10=2^2-7z+3 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8z^2+7z-17=0

a = 8; b = 7; c = -17;
Δ = b2-4ac
Δ = 72-4·8·(-17)
Δ = 593
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{-(7)-\sqrt{593}}{2*8}=\frac{-7-\sqrt{593}}{16}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{593}}{2*8}=\frac{-7+\sqrt{593}}{16}
$