7x^2-30x+4=0

Solution for 7x^2-30x+4=0 equation:

7x^2-30x+4=0

a = 7; b = -30; c = +4;
Δ = b2-4ac
Δ = -302-4·7·4
Δ = 788
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:

$\sqrt{\Delta}=\sqrt{788}=\sqrt{4*197}=\sqrt{4}*\sqrt{197}=2\sqrt{197}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{197}}{2*7}=\frac{30-2\sqrt{197}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{197}}{2*7}=\frac{30+2\sqrt{197}}{14}
$