78=4x2+14x

Solution for 78=4x2+14x equation:

78=4x^2+14x

We move all terms to the left:

78-(4x^2+14x)=0

We get rid of parentheses

-4x^2-14x+78=0

a = -4; b = -14; c = +78;
Δ = b2-4ac
Δ = -142-4·(-4)·78
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-38}{2*-4}=\frac{-24}{-8}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+38}{2*-4}=\frac{52}{-8}
=-6+1/2
$