G(x)=7x^2-567

Solution for G(x)=7x^2-567 equation:

(G)=7G^2-567

We move all terms to the left:

(G)-(7G^2-567)=0

We get rid of parentheses

-7G^2+G+567=0

a = -7; b = 1; c = +567;
Δ = b2-4ac
Δ = 12-4·(-7)·567
Δ = 15877
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{-(1)-\sqrt{15877}}{2*-7}=\frac{-1-\sqrt{15877}}{-14}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{15877}}{2*-7}=\frac{-1+\sqrt{15877}}{-14}
$