(3x+20)(2x+30)=70

Solution for (3x+20)(2x+30)=70 equation:

(3x+20)(2x+30)=70

We move all terms to the left:

(3x+20)(2x+30)-(70)=0

We multiply parentheses ..

(+6x^2+90x+40x+600)-70=0

We get rid of parentheses

6x^2+90x+40x+600-70=0

We add all the numbers together, and all the variables

6x^2+130x+530=0

a = 6; b = 130; c = +530;
Δ = b2-4ac
Δ = 1302-4·6·530
Δ = 4180
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:

$\sqrt{\Delta}=\sqrt{4180}=\sqrt{4*1045}=\sqrt{4}*\sqrt{1045}=2\sqrt{1045}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-2\sqrt{1045}}{2*6}=\frac{-130-2\sqrt{1045}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+2\sqrt{1045}}{2*6}=\frac{-130+2\sqrt{1045}}{12}
$