(x+10)(3x+10)=76

Solution for (x+10)(3x+10)=76 equation:

(x+10)(3x+10)=76

We move all terms to the left:

(x+10)(3x+10)-(76)=0

We multiply parentheses ..

(+3x^2+10x+30x+100)-76=0

We get rid of parentheses

3x^2+10x+30x+100-76=0

We add all the numbers together, and all the variables

3x^2+40x+24=0

a = 3; b = 40; c = +24;
Δ = b2-4ac
Δ = 402-4·3·24
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{82}}{2*3}=\frac{-40-4\sqrt{82}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{82}}{2*3}=\frac{-40+4\sqrt{82}}{6}
$