4x2+5x=10

Solution for 4x2+5x=10 equation:

4x^2+5x=10

We move all terms to the left:

4x^2+5x-(10)=0

a = 4; b = 5; c = -10;
Δ = b2-4ac
Δ = 52-4·4·(-10)
Δ = 185
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{-(5)-\sqrt{185}}{2*4}=\frac{-5-\sqrt{185}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{185}}{2*4}=\frac{-5+\sqrt{185}}{8}
$