7*x^2-270x+400=0

Solution for 7*x^2-270x+400=0 equation:

7x^2-270x+400=0

a = 7; b = -270; c = +400;
Δ = b2-4ac
Δ = -2702-4·7·400
Δ = 61700
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:

$\sqrt{\Delta}=\sqrt{61700}=\sqrt{100*617}=\sqrt{100}*\sqrt{617}=10\sqrt{617}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-10\sqrt{617}}{2*7}=\frac{270-10\sqrt{617}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+10\sqrt{617}}{2*7}=\frac{270+10\sqrt{617}}{14}
$