4x^2-15x=19=5x+10

Solution for 4x^2-15x=19=5x+10 equation:

4x^2-15x=19=5x+10

We move all terms to the left:

4x^2-15x-(19)=0

a = 4; b = -15; c = -19;
Δ = b2-4ac
Δ = -152-4·4·(-19)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-23}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+23}{2*4}=\frac{38}{8}
=4+3/4
$