G(x)=(3X-4)(8X-7)

Solution for G(x)=(3X-4)(8X-7) equation:

(G)=(3G-4)(8G-7)

We move all terms to the left:

(G)-((3G-4)(8G-7))=0

We multiply parentheses ..

-((+24G^2-21G-32G+28))+G=0


We calculate terms in parentheses: -((+24G^2-21G-32G+28)), so:

(+24G^2-21G-32G+28)

We get rid of parentheses

24G^2-21G-32G+28

We add all the numbers together, and all the variables

24G^2-53G+28

Back to the equation:

-(24G^2-53G+28)


We add all the numbers together, and all the variables

G-(24G^2-53G+28)=0

We get rid of parentheses

-24G^2+G+53G-28=0

We add all the numbers together, and all the variables

-24G^2+54G-28=0

a = -24; b = 54; c = -28;
Δ = b2-4ac
Δ = 542-4·(-24)·(-28)
Δ = 228
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{57}}{2*-24}=\frac{-54-2\sqrt{57}}{-48}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{57}}{2*-24}=\frac{-54+2\sqrt{57}}{-48}
$