(4g-1)(2g+7)=0

Solution for (4g-1)(2g+7)=0 equation:

(4g-1)(2g+7)=0

We multiply parentheses ..

(+8g^2+28g-2g-7)=0

We get rid of parentheses

8g^2+28g-2g-7=0

We add all the numbers together, and all the variables

8g^2+26g-7=0

a = 8; b = 26; c = -7;
Δ = b2-4ac
Δ = 262-4·8·(-7)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-30}{2*8}=\frac{-56}{16}
=-3+1/2
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+30}{2*8}=\frac{4}{16}
=1/4
$