4x^2+5x=152

Solution for 4x^2+5x=152 equation:

4x^2+5x=152

We move all terms to the left:

4x^2+5x-(152)=0

a = 4; b = 5; c = -152;
Δ = b2-4ac
Δ = 52-4·4·(-152)
Δ = 2457
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:

$\sqrt{\Delta}=\sqrt{2457}=\sqrt{9*273}=\sqrt{9}*\sqrt{273}=3\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{273}}{2*4}=\frac{-5-3\sqrt{273}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{273}}{2*4}=\frac{-5+3\sqrt{273}}{8}
$