10x^2-90x+14=0

Solution for 10x^2-90x+14=0 equation:

10x^2-90x+14=0

a = 10; b = -90; c = +14;
Δ = b2-4ac
Δ = -902-4·10·14
Δ = 7540
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:

$\sqrt{\Delta}=\sqrt{7540}=\sqrt{4*1885}=\sqrt{4}*\sqrt{1885}=2\sqrt{1885}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{1885}}{2*10}=\frac{90-2\sqrt{1885}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{1885}}{2*10}=\frac{90+2\sqrt{1885}}{20}
$