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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

18x^2+174x+42x+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}
$