x(2x+3)=152

Solution for x(2x+3)=152 equation:

x(2x+3)=152

We move all terms to the left:

x(2x+3)-(152)=0

We multiply parentheses

2x^2+3x-152=0

a = 2; b = 3; c = -152;
Δ = b2-4ac
Δ = 32-4·2·(-152)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-35}{2*2}=\frac{-38}{4}
=-9+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+35}{2*2}=\frac{32}{4}
=8
$