6x*x+30x=40

Solution for 6x*x+30x=40 equation:

6x*x+30x=40

We move all terms to the left:

6x*x+30x-(40)=0

We add all the numbers together, and all the variables

30x+6x*x-40=0

Wy multiply elements

6x^2+30x-40=0

a = 6; b = 30; c = -40;
Δ = b2-4ac
Δ = 302-4·6·(-40)
Δ = 1860
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:

$\sqrt{\Delta}=\sqrt{1860}=\sqrt{4*465}=\sqrt{4}*\sqrt{465}=2\sqrt{465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{465}}{2*6}=\frac{-30-2\sqrt{465}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{465}}{2*6}=\frac{-30+2\sqrt{465}}{12}
$