7-24x+7x^2=0

Solution for 7-24x+7x^2=0 equation:

7-24x+7x^2=0

a = 7; b = -24; c = +7;
Δ = b2-4ac
Δ = -242-4·7·7
Δ = 380
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{95}}{2*7}=\frac{24-2\sqrt{95}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{95}}{2*7}=\frac{24+2\sqrt{95}}{14}
$