5x(3x-4)+4=114

Solution for 5x(3x-4)+4=114 equation:

5x(3x-4)+4=114

We move all terms to the left:

5x(3x-4)+4-(114)=0

We add all the numbers together, and all the variables

5x(3x-4)-110=0

We multiply parentheses

15x^2-20x-110=0

a = 15; b = -20; c = -110;
Δ = b2-4ac
Δ = -202-4·15·(-110)
Δ = 7000
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:

$\sqrt{\Delta}=\sqrt{7000}=\sqrt{100*70}=\sqrt{100}*\sqrt{70}=10\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10\sqrt{70}}{2*15}=\frac{20-10\sqrt{70}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10\sqrt{70}}{2*15}=\frac{20+10\sqrt{70}}{30}
$