5x(7x+16)=90

Solution for 5x(7x+16)=90 equation:

5x(7x+16)=90

We move all terms to the left:

5x(7x+16)-(90)=0

We multiply parentheses

35x^2+80x-90=0

a = 35; b = 80; c = -90;
Δ = b2-4ac
Δ = 802-4·35·(-90)
Δ = 19000
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:

$\sqrt{\Delta}=\sqrt{19000}=\sqrt{100*190}=\sqrt{100}*\sqrt{190}=10\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-10\sqrt{190}}{2*35}=\frac{-80-10\sqrt{190}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+10\sqrt{190}}{2*35}=\frac{-80+10\sqrt{190}}{70}
$