5x(4x+6)+113+90=540

Solution for 5x(4x+6)+113+90=540 equation:

5x(4x+6)+113+90=540

We move all terms to the left:

5x(4x+6)+113+90-(540)=0

We add all the numbers together, and all the variables

5x(4x+6)-337=0

We multiply parentheses

20x^2+30x-337=0

a = 20; b = 30; c = -337;
Δ = b2-4ac
Δ = 302-4·20·(-337)
Δ = 27860
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:

$\sqrt{\Delta}=\sqrt{27860}=\sqrt{4*6965}=\sqrt{4}*\sqrt{6965}=2\sqrt{6965}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{6965}}{2*20}=\frac{-30-2\sqrt{6965}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{6965}}{2*20}=\frac{-30+2\sqrt{6965}}{40}
$