5x(x+9)-4=51

Solution for 5x(x+9)-4=51 equation:

5x(x+9)-4=51

We move all terms to the left:

5x(x+9)-4-(51)=0

We add all the numbers together, and all the variables

5x(x+9)-55=0

We multiply parentheses

5x^2+45x-55=0

a = 5; b = 45; c = -55;
Δ = b2-4ac
Δ = 452-4·5·(-55)
Δ = 3125
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:

$\sqrt{\Delta}=\sqrt{3125}=\sqrt{625*5}=\sqrt{625}*\sqrt{5}=25\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-25\sqrt{5}}{2*5}=\frac{-45-25\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+25\sqrt{5}}{2*5}=\frac{-45+25\sqrt{5}}{10}
$