4x^2+10x=75

Solution for 4x^2+10x=75 equation:

4x^2+10x=75

We move all terms to the left:

4x^2+10x-(75)=0

a = 4; b = 10; c = -75;
Δ = b2-4ac
Δ = 102-4·4·(-75)
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{13}}{2*4}=\frac{-10-10\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{13}}{2*4}=\frac{-10+10\sqrt{13}}{8}
$