10z^2+7z+4=3

Solution for 10z^2+7z+4=3 equation:

10z^2+7z+4=3

We move all terms to the left:

10z^2+7z+4-(3)=0

We add all the numbers together, and all the variables

10z^2+7z+1=0

a = 10; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·10·1
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3}{2*10}=\frac{-10}{20}
=-1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3}{2*10}=\frac{-4}{20}
=-1/5
$