(1+4x)(2x+5)=90

Solution for (1+4x)(2x+5)=90 equation:

(1+4x)(2x+5)=90

We move all terms to the left:

(1+4x)(2x+5)-(90)=0

We add all the numbers together, and all the variables

(4x+1)(2x+5)-90=0

We multiply parentheses ..

(+8x^2+20x+2x+5)-90=0

We get rid of parentheses

8x^2+20x+2x+5-90=0

We add all the numbers together, and all the variables

8x^2+22x-85=0

a = 8; b = 22; c = -85;
Δ = b2-4ac
Δ = 222-4·8·(-85)
Δ = 3204
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:

$\sqrt{\Delta}=\sqrt{3204}=\sqrt{36*89}=\sqrt{36}*\sqrt{89}=6\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-6\sqrt{89}}{2*8}=\frac{-22-6\sqrt{89}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+6\sqrt{89}}{2*8}=\frac{-22+6\sqrt{89}}{16}
$