5x2+16x=15

Solution for 5x2+16x=15 equation:

5x^2+16x=15

We move all terms to the left:

5x^2+16x-(15)=0

a = 5; b = 16; c = -15;
Δ = b2-4ac
Δ = 162-4·5·(-15)
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{139}}{2*5}=\frac{-16-2\sqrt{139}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{139}}{2*5}=\frac{-16+2\sqrt{139}}{10}
$