5x(3x+1)=35

Solution for 5x(3x+1)=35 equation:

5x(3x+1)=35

We move all terms to the left:

5x(3x+1)-(35)=0

We multiply parentheses

15x^2+5x-35=0

a = 15; b = 5; c = -35;
Δ = b2-4ac
Δ = 52-4·15·(-35)
Δ = 2125
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:

$\sqrt{\Delta}=\sqrt{2125}=\sqrt{25*85}=\sqrt{25}*\sqrt{85}=5\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{85}}{2*15}=\frac{-5-5\sqrt{85}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{85}}{2*15}=\frac{-5+5\sqrt{85}}{30}
$