14x(16x+15)=45

Solution for 14x(16x+15)=45 equation:

14x(16x+15)=45

We move all terms to the left:

14x(16x+15)-(45)=0

We multiply parentheses

224x^2+210x-45=0

a = 224; b = 210; c = -45;
Δ = b2-4ac
Δ = 2102-4·224·(-45)
Δ = 84420
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:

$\sqrt{\Delta}=\sqrt{84420}=\sqrt{36*2345}=\sqrt{36}*\sqrt{2345}=6\sqrt{2345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(210)-6\sqrt{2345}}{2*224}=\frac{-210-6\sqrt{2345}}{448}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(210)+6\sqrt{2345}}{2*224}=\frac{-210+6\sqrt{2345}}{448}
$