7x^2-24x+15=0

Solution for 7x^2-24x+15=0 equation:

7x^2-24x+15=0

a = 7; b = -24; c = +15;
Δ = b2-4ac
Δ = -242-4·7·15
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{39}}{2*7}=\frac{24-2\sqrt{39}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{39}}{2*7}=\frac{24+2\sqrt{39}}{14}
$