4x2=47x+126

Solution for 4x2=47x+126 equation:

4x^2=47x+126

We move all terms to the left:

4x^2-(47x+126)=0

We get rid of parentheses

4x^2-47x-126=0

a = 4; b = -47; c = -126;
Δ = b2-4ac
Δ = -472-4·4·(-126)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-65}{2*4}=\frac{-18}{8}
=-2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+65}{2*4}=\frac{112}{8}
=14
$