5x(2x-7)+5=30

Solution for 5x(2x-7)+5=30 equation:

5x(2x-7)+5=30

We move all terms to the left:

5x(2x-7)+5-(30)=0

We add all the numbers together, and all the variables

5x(2x-7)-25=0

We multiply parentheses

10x^2-35x-25=0

a = 10; b = -35; c = -25;
Δ = b2-4ac
Δ = -352-4·10·(-25)
Δ = 2225
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:

$\sqrt{\Delta}=\sqrt{2225}=\sqrt{25*89}=\sqrt{25}*\sqrt{89}=5\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5\sqrt{89}}{2*10}=\frac{35-5\sqrt{89}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5\sqrt{89}}{2*10}=\frac{35+5\sqrt{89}}{20}
$