G(x)=5x^2-24x+3

Solution for G(x)=5x^2-24x+3 equation:

(G)=5G^2-24G+3

We move all terms to the left:

(G)-(5G^2-24G+3)=0

We get rid of parentheses

-5G^2+G+24G-3=0

We add all the numbers together, and all the variables

-5G^2+25G-3=0

a = -5; b = 25; c = -3;
Δ = b2-4ac
Δ = 252-4·(-5)·(-3)
Δ = 565
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{565}}{2*-5}=\frac{-25-\sqrt{565}}{-10}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{565}}{2*-5}=\frac{-25+\sqrt{565}}{-10}
$