4x^2-28x=46

Solution for 4x^2-28x=46 equation:

4x^2-28x=46

We move all terms to the left:

4x^2-28x-(46)=0

a = 4; b = -28; c = -46;
Δ = b2-4ac
Δ = -282-4·4·(-46)
Δ = 1520
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:

$\sqrt{\Delta}=\sqrt{1520}=\sqrt{16*95}=\sqrt{16}*\sqrt{95}=4\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{95}}{2*4}=\frac{28-4\sqrt{95}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{95}}{2*4}=\frac{28+4\sqrt{95}}{8}
$