24=4x2+14x

Solution for 24=4x2+14x equation:

24=4x^2+14x

We move all terms to the left:

24-(4x^2+14x)=0

We get rid of parentheses

-4x^2-14x+24=0

a = -4; b = -14; c = +24;
Δ = b2-4ac
Δ = -142-4·(-4)·24
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{145}}{2*-4}=\frac{14-2\sqrt{145}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{145}}{2*-4}=\frac{14+2\sqrt{145}}{-8}
$