4x^2-82x+78=0

Solution for 4x^2-82x+78=0 equation:

4x^2-82x+78=0

a = 4; b = -82; c = +78;
Δ = b2-4ac
Δ = -822-4·4·78
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-74}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+74}{2*4}=\frac{156}{8}
=19+1/2
$