12x^2-70x+75=0

Solution for 12x^2-70x+75=0 equation:

12x^2-70x+75=0

a = 12; b = -70; c = +75;
Δ = b2-4ac
Δ = -702-4·12·75
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-10\sqrt{13}}{2*12}=\frac{70-10\sqrt{13}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+10\sqrt{13}}{2*12}=\frac{70+10\sqrt{13}}{24}
$