(x+4)(3x+10)=90

Solution for (x+4)(3x+10)=90 equation:

(x+4)(3x+10)=90

We move all terms to the left:

(x+4)(3x+10)-(90)=0

We multiply parentheses ..

(+3x^2+10x+12x+40)-90=0

We get rid of parentheses

3x^2+10x+12x+40-90=0

We add all the numbers together, and all the variables

3x^2+22x-50=0

a = 3; b = 22; c = -50;
Δ = b2-4ac
Δ = 222-4·3·(-50)
Δ = 1084
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:

$\sqrt{\Delta}=\sqrt{1084}=\sqrt{4*271}=\sqrt{4}*\sqrt{271}=2\sqrt{271}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{271}}{2*3}=\frac{-22-2\sqrt{271}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{271}}{2*3}=\frac{-22+2\sqrt{271}}{6}
$