5x(7x+3)=15

Solution for 5x(7x+3)=15 equation:

5x(7x+3)=15

We move all terms to the left:

5x(7x+3)-(15)=0

We multiply parentheses

35x^2+15x-15=0

a = 35; b = 15; c = -15;
Δ = b2-4ac
Δ = 152-4·35·(-15)
Δ = 2325
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:

$\sqrt{\Delta}=\sqrt{2325}=\sqrt{25*93}=\sqrt{25}*\sqrt{93}=5\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{93}}{2*35}=\frac{-15-5\sqrt{93}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{93}}{2*35}=\frac{-15+5\sqrt{93}}{70}
$