4x^2-78=11x

Solution for 4x^2-78=11x equation:

4x^2-78=11x

We move all terms to the left:

4x^2-78-(11x)=0

a = 4; b = -11; c = -78;
Δ = b2-4ac
Δ = -112-4·4·(-78)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-37}{2*4}=\frac{-26}{8}
=-3+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+37}{2*4}=\frac{48}{8}
=6
$