90=(2x+6)(5x+21)

Solution for 90=(2x+6)(5x+21) equation:

90=(2x+6)(5x+21)

We move all terms to the left:

90-((2x+6)(5x+21))=0

We multiply parentheses ..

-((+10x^2+42x+30x+126))+90=0


We calculate terms in parentheses: -((+10x^2+42x+30x+126)), so:

(+10x^2+42x+30x+126)

We get rid of parentheses

10x^2+42x+30x+126

We add all the numbers together, and all the variables

10x^2+72x+126

Back to the equation:

-(10x^2+72x+126)


We get rid of parentheses

-10x^2-72x-126+90=0

We add all the numbers together, and all the variables

-10x^2-72x-36=0

a = -10; b = -72; c = -36;
Δ = b2-4ac
Δ = -722-4·(-10)·(-36)
Δ = 3744
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:

$\sqrt{\Delta}=\sqrt{3744}=\sqrt{144*26}=\sqrt{144}*\sqrt{26}=12\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{26}}{2*-10}=\frac{72-12\sqrt{26}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{26}}{2*-10}=\frac{72+12\sqrt{26}}{-20}
$