5x(2x+3)+3(5x-2)=84

Solution for 5x(2x+3)+3(5x-2)=84 equation:

5x(2x+3)+3(5x-2)=84

We move all terms to the left:

5x(2x+3)+3(5x-2)-(84)=0

We multiply parentheses

10x^2+15x+15x-6-84=0

We add all the numbers together, and all the variables

10x^2+30x-90=0

a = 10; b = 30; c = -90;
Δ = b2-4ac
Δ = 302-4·10·(-90)
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30\sqrt{5}}{2*10}=\frac{-30-30\sqrt{5}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30\sqrt{5}}{2*10}=\frac{-30+30\sqrt{5}}{20}
$