(4x+3)(4x+7)=90

Solution for (4x+3)(4x+7)=90 equation:

(4x+3)(4x+7)=90

We move all terms to the left:

(4x+3)(4x+7)-(90)=0

We multiply parentheses ..

(+16x^2+28x+12x+21)-90=0

We get rid of parentheses

16x^2+28x+12x+21-90=0

We add all the numbers together, and all the variables

16x^2+40x-69=0

a = 16; b = 40; c = -69;
Δ = b2-4ac
Δ = 402-4·16·(-69)
Δ = 6016
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:

$\sqrt{\Delta}=\sqrt{6016}=\sqrt{64*94}=\sqrt{64}*\sqrt{94}=8\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{94}}{2*16}=\frac{-40-8\sqrt{94}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{94}}{2*16}=\frac{-40+8\sqrt{94}}{32}
$