10x^2=3x+4

Solution for 10x^2=3x+4 equation:

10x^2=3x+4

We move all terms to the left:

10x^2-(3x+4)=0

We get rid of parentheses

10x^2-3x-4=0

a = 10; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·10·(-4)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-13}{2*10}=\frac{-10}{20}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+13}{2*10}=\frac{16}{20}
=4/5
$