(x)(2x+1)=75

Solution for (x)(2x+1)=75 equation:

(x)(2x+1)=75

We move all terms to the left:

(x)(2x+1)-(75)=0

We multiply parentheses

2x^2+x-75=0

a = 2; b = 1; c = -75;
Δ = b2-4ac
Δ = 12-4·2·(-75)
Δ = 601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{601}}{2*2}=\frac{-1-\sqrt{601}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{601}}{2*2}=\frac{-1+\sqrt{601}}{4}
$