x(2x+3)=702

Solution for x(2x+3)=702 equation:

x(2x+3)=702

We move all terms to the left:

x(2x+3)-(702)=0

We multiply parentheses

2x^2+3x-702=0

a = 2; b = 3; c = -702;
Δ = b2-4ac
Δ = 32-4·2·(-702)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-75}{2*2}=\frac{-78}{4}
=-19+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+75}{2*2}=\frac{72}{4}
=18
$