(6x+29)(x+5)=90

Solution for (6x+29)(x+5)=90 equation:

(6x+29)(x+5)=90

We move all terms to the left:

(6x+29)(x+5)-(90)=0

We multiply parentheses ..

(+6x^2+30x+29x+145)-90=0

We get rid of parentheses

6x^2+30x+29x+145-90=0

We add all the numbers together, and all the variables

6x^2+59x+55=0

a = 6; b = 59; c = +55;
Δ = b2-4ac
Δ = 592-4·6·55
Δ = 2161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-\sqrt{2161}}{2*6}=\frac{-59-\sqrt{2161}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+\sqrt{2161}}{2*6}=\frac{-59+\sqrt{2161}}{12}
$