90=(6x+14)(3x+29)

Solution for 90=(6x+14)(3x+29) equation:

90=(6x+14)(3x+29)

We move all terms to the left:

90-((6x+14)(3x+29))=0

We multiply parentheses ..

-((+18x^2+174x+42x+406))+90=0


We calculate terms in parentheses: -((+18x^2+174x+42x+406)), so:

(+18x^2+174x+42x+406)

We get rid of parentheses

18x^2+174x+42x+406

We add all the numbers together, and all the variables

18x^2+216x+406

Back to the equation:

-(18x^2+216x+406)


We get rid of parentheses

-18x^2-216x-406+90=0

We add all the numbers together, and all the variables

-18x^2-216x-316=0

a = -18; b = -216; c = -316;
Δ = b2-4ac
Δ = -2162-4·(-18)·(-316)
Δ = 23904
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:

$\sqrt{\Delta}=\sqrt{23904}=\sqrt{144*166}=\sqrt{144}*\sqrt{166}=12\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-12\sqrt{166}}{2*-18}=\frac{216-12\sqrt{166}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+12\sqrt{166}}{2*-18}=\frac{216+12\sqrt{166}}{-36}
$