(3x+7)(5x+3)=90

Solution for (3x+7)(5x+3)=90 equation:

(3x+7)(5x+3)=90

We move all terms to the left:

(3x+7)(5x+3)-(90)=0

We multiply parentheses ..

(+15x^2+9x+35x+21)-90=0

We get rid of parentheses

15x^2+9x+35x+21-90=0

We add all the numbers together, and all the variables

15x^2+44x-69=0

a = 15; b = 44; c = -69;
Δ = b2-4ac
Δ = 442-4·15·(-69)
Δ = 6076
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:

$\sqrt{\Delta}=\sqrt{6076}=\sqrt{196*31}=\sqrt{196}*\sqrt{31}=14\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-14\sqrt{31}}{2*15}=\frac{-44-14\sqrt{31}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+14\sqrt{31}}{2*15}=\frac{-44+14\sqrt{31}}{30}
$